EDITH BROWN CLEMENT, Circuit Judge:

United Steelworkers International Union, Local 13-0555 ("USW") appeals the district court's vacatur of an arbitral award against ConocoPhillips, Inc. ("Conoco") involving dismissal of a refinery employee who failed a workplace drug test. We AFFIRM.

FACTS AND PROCEEDINGS

USW member Dave Buller was a refinery operator at a Conoco refinery in Lake Charles, Louisiana. On June 14, 2010, he was subject to a random drug test at work, and tested above the allowed threshold for hydrocodone. Conoco terminated him, pursuant to a company policy providing for termination of those who fail drug tests. Buller claimed that the test result had been caused by several doses of a prescription cough medication, which had been prescribed for him several years earlier and had long since expired.

The collective bargaining agreement ("CBA") between Conoco and USW provides for arbitration of grievances and of matters relating to the interpretation and implementation of the CBA. Section 2-2 of that agreement states:

USW brought an arbitration action against Conoco on Buller's behalf for wrongful termination, despite section 2-2's language providing that "[d]ischarge for a confirmed positive test under the substance abuse policy shall not be subject to grievance or arbitration" except with respect to "the integrity of the chain of custody." USW argues that the grievance is for unjust discharge, and was properly before the arbitrator.

At the start of the arbitration hearing, Conoco contested the arbitrability of the dispute, stating that, because Buller had been discharged for substance abuse, the dispute was not arbitrable, except with respect to the chain of custody. The arbitrator stated that he would nevertheless hear the merits of the case before deciding the arbitrability question. Conoco proceeded to present its case, which focused primarily on the chain of custody of the drug test evidence.

As the union began presenting its case, which was not limited to the chain of custody, Conoco repeatedly objected on the ground that the arbitrator was exceeding his jurisdiction under the CBA. Conoco eventually logged a continuing objection to USW's case, stating: "Can my objection be continuing about this because I have objected to ... the various provisions of the Contract and can you arbitrate anything more than just what the Contract says." At the end of the proceedings, the following exchange occurred regarding the scope of the arbitration:

Following briefing on the issues discussed at the arbitration proceeding, the arbitrator: (1) found that he did have the authority to consider this dispute, (2) determined that the dispute was arbitrable, and (3) entered an award for Buller, holding that Buller's termination had been wrongful.

Conoco filed the instant action in the district court, seeking vacatur of the arbitral award. The parties filed cross-motions for summary judgment. Conoco contested the arbitrator's determination that the merits of the discharge were arbitrable, arguing that it (1) never consented to arbitrate a discharge for a positive drug test, and (2) never agreed to allow the arbitrator to decide whether the dispute was arbitrable. USW argued that Conoco implicitly agreed to submit the question of arbitrability to the arbitrator, and was therefore bound by its (1) determination that the dispute was arbitrable and (2) subsequent award in favor of USW.

The district court granted Conoco's motion, holding that "there was no clear and unmistakable agreement" to submit the question of arbitrability to the arbitrator himself. It vacated the arbitration and the result of the arbitration, and USW appealed.

STANDARD OF REVIEW

We review a district court's judgment on arbitrability awards "like review of any other district court decision finding an agreement between parties, e.g., accepting findings of fact that are not `clearly erroneous' but deciding questions of law de novo." First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 947-48, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995).

DISCUSSION

There are three types of disputes concerning arbitration: (1) the merits of the dispute; (2) whether the parties agreed to arbitrate the merits; and (3) who has "the primary power to decide" whether the parties agreed to arbitrate the merits. Id. at 942, 115 S.Ct. 1920. Only the second and third questions are at issue in this case.

Arbitration is "simply a matter of contract between the parties; it is a way to resolve those disputes-but only those disputes-that the parties have agreed to submit to arbitration." Id. at 943, 115 S.Ct. 1920. If an issue has been submitted to an arbitrator, a court "will set that decision aside only in very unusual circumstances," such as fraud, manifest disregard of the law, corruption, undue means, and the arbitrator overstepping its powers. Id. at 942, 115 S.Ct. 1920. But if an issue has not been submitted to the arbitrator, the "party who has not agreed to arbitrate will normally have a right to a court's decision about the merits of its dispute." Id.

The primary issue on appeal is whether the parties agreed to submit the question of "who has the power to decide whether an issue is arbitrable" to the arbitrator. USW, as the party contending that Conoco agreed to submit that question to the arbitrator, "bear[s] the burden of demonstrating clearly and unmistakably that the parties agreed to have the arbitrator decide that threshold question of arbitrability." Gen. Motors Corp. v. Pamela Equities Corp., 146 F.3d 242, 249 (5th Cir.1998). If USW cannot show that the parties "clearly and unmistakably" submitted the arbitrability question itself to the arbitrator, then the "court should decide that question just as it would decide any other question that the parties did not submit to arbitration, namely, independently." First Options, 514 U.S. at 943, 115 S.Ct. 1920.

I. Did the parties "clearly and unmistakably" agree to submit the question of "who has the power to decide whether an issue is arbitrable" to the arbitrator himself?

The threshold and potentially dispositive issue is whether the parties granted the arbitrator the power to determine whether Buller's discharge was arbitrable. Although the question of whether a particular issue is arbitrable errs in favor of arbitration, "courts should not assume that the parties agreed to arbitrate arbitrability unless there is `clea[r] and unmistakabl[e]' evidence that they did so." Id. at 944, 115 S.Ct. 1920. This standard applies "regardless of whether the parties have entered into a pre-dispute arbitration contract." Pamela, 146 F.3d at 248 ("[W]e conclude that the `clear and unmistakable evidence' standard applies whenever one party to a dispute contends that the other party agreed to submit to an arbitrator the question of whether that arbitrator has been authorized to resolve the merits of their dispute, regardless of whether the parties have entered a pre-dispute arbitration contract.").

The Supreme Court has defined a "clear willingness to arbitrate" arbitrability as "a willingness to be effectively bound by the arbitrator's decision on that point." Id. at 946, 115 S.Ct. 1920. Such a "willingness to be effectively bound" is not demonstrated by "merely arguing the arbitrability issue to an arbitrator." Id. Nor do silence and ambiguity support a "willingness to be effectively bound"; those circumstances favor submitting the question to the courts, lest the arbitrator "force unwilling parties to arbitrate a matter they reasonably would have thought a judge, not an arbitrator, would decide." Id. at 945, 115 S.Ct. 1920.

USW has not borne its burden in demonstrating Conoco's clear and unmistakable intent to be bound by the arbitrator's decision on arbitrability. It is undisputed that the CBA does not expressly submit the question of arbitrability to the arbitrator. USW instead argues that Conoco's conduct during the arbitration hearing and statements in its briefs demonstrate that it "readily submitted the question" of arbitrability to the arbitrator. But the record on this point does not clearly and unmistakably support that conclusion. At best, Conoco's actions and statements are ambiguous; at worst, they demonstrate a clear rejection of the arbitrator's authority to determine arbitrability.

In First Options, the Kaplans — in their personal capacity — filed a written memorandum with the arbitrator objecting to its jurisdiction over their dispute. Rather than finding that filing an objection with the arbitrator constituted consent to be bound by its decision on arbitrability, the Supreme Court found that, "insofar as the Kaplans were forcefully objecting to the arbitrators deciding their dispute ... one naturally would think that they did not want the arbitrators to have binding authority over them." Id. at 946, 115 S.Ct. 1920. The Court found support for this conclusion from the "obvious explanation for the Kaplans' presence before the arbitrators," namely that their wholly owned subsidiary was before the arbitrator in the same matter. Id.

Similarly, Conoco repeatedly objected to the arbitrator's determination of any issue beyond "chain of custody." It objected in its opening statement to the arbitrator's jurisdiction over Buller's discharge, but acknowledged jurisdiction over the chain of custody. Conoco objected throughout USW's presentation that the issue of discharge was beyond the arbitrator's jurisdiction, and eventually made a continuing objection to the presentation of USW's case, stating: "Can my objection be continuing about this because I have objected to ... the various provisions of the Contract and can you arbitrate anything more than just what the Contract says." Finally, at the end of the hearing, counsel for Conoco explicitly stated that while the chain of custody was properly before the arbitrator, "we don't think anything else is properly before the Arbitrator." And just as the Kaplans had an obvious explanation for appearing before the arbitrator, Conoco was there to litigate the chain of custody, a potential source of relief for Buller under the CBA.

USW's arguments focus on Conoco (1) arguing arbitrability to the arbitrator, (2) failing to object to the arbitrator's indications that it would address arbitrability, and (3) presenting argument beyond mere chain of custody at the hearing. None of this evidences a clear and unmistakable intent to be bound by the arbitrator's decision on arbitrability. As the Supreme Court stated in First Options, "merely arguing the arbitrability issue to an arbitrator" is not enough to show clear and unmistakable intent. Id. The fact that Conoco raised an issue of jurisdiction at the hearing and submitted briefing to dissuade the arbitrator from addressing the merits of the discharge does not indicate that it intended to be bound by that determination. "Merely arguing" the issue is not enough, even if the issue is competently and consistently presented.

USW also notes Conoco's failure to object to certain indications that the arbitrator would consider the issue of arbitrability, particularly its statement that: "To the matter of arbitrability, I'll go ahead and hear the merits and then I'll decide the Arbitrability later. And if I get to the merits, I get to the merits." It also argues that all of Conoco's objections referred to whether the question was arbitrable, not whether the arbitrator had the power to decide that issue, "confirming that the Company acquiesced in toto to the arbitrator's resolving ... the question of arbitrability." But in determining whether parties have agreed to arbitrate arbitrability, ambiguity and silence favor having that question decided by the courts, not the arbitrator. See id. at 944-45, 115 S.Ct. 1920. USW's argument that Conoco's consent can be inferred from its silence contradicts the holding of First Options and flips the burden of proof on its head. Rather than asking whether USW met its burden of "clearly and unmistakably" demonstrating the parties' agreement to arbitrate arbitrability, USW contends — in both its brief and at oral argument — that the question is whether Conoco "clearly objected and reserved its right to contest arbitrability." That is not the standard announced in First Options, and Conoco's alleged failure to object is insufficient to demonstrate its intent to be bound by the arbitrator's decision on arbitrability.

Similarly, to the extent that Conoco presented arguments — either in its case-in-chief or on rebuttal — that extended to the merits of the dispute, it cannot be the case that merely countering your opponent's case demonstrates an intent to be bound by the arbitrator's decision. Even believing that the arbitrator lacked jurisdiction and with full intent to appeal, it would be prudent for Conoco to address USW's merits arguments, just in case it lost its jurisdictional argument and lost again on appeal. Indeed, the district court could uphold Conoco's jurisdictional challenge — vesting the "arbitrability" decision in the courts — but still find the dispute arbitrable and uphold the arbitration award in favor of USW. When weighed against its consistent objections to arbitrating anything beyond the chain of custody, Conoco's decision to address issues beyond the arbitrability of arbitrability does not clearly and unmistakably demonstrate an intent to be bound by the arbitrator's decision.

USW relies on two non-binding cases in support of its position that Conoco clearly and unmistakably consented to have the arbitrator decide arbitrability. In Rock-Tenn Company v. United Paperworkers International Union AFL-CIO, the Fourth Circuit found clear and unmistakable consent where a party (1) voluntarily submitted to arbitration of the dispute, (2) vigorously participated in "on the merits debate during the arbitration proceedings," and (3) utterly failed "during those proceedings to challenge the arbitrator's authority to determine the dispute, or even to preserve the issue for resolution by the court." 184 F.3d 330, 334 (4th Cir.1999). Similarly, in Cleveland Electric Illuminating Company v. Utility Workers Union of America, the Sixth Circuit found the objecting party's failure to argue at arbitration "that the arbitrator had no authority to decide the issue of arbitrability" sufficient to demonstrate clear and unmistakable consent to be bound by the arbitrator's decision on arbitrability. 440 F.3d 809, 811 (6th Cir.2006).

These cases are easily distinguishable. Both Rock-Tenn and Cleveland Electric rely heavily on the parties' failure to object to the arbitrator's power to decide arbitrability during the hearing. Conoco's attorney arguably objected to arbitrating arbitrability at two different points during hearing, stating: (1) "Can my objection be continuing about this because I have objected to ... the various provisions of the Contract and can you arbitrate anything more than just what the Contract says"; and (2) besides chain of custody, "we don't think anything else is properly before the Arbitrator." On their terms, Conoco appears to be objecting to the arbitrator's authority to decide anything not explicitly spelled out in the CBA — such as who has the power to decide arbitrability — or "anything" besides chain of custody. At the very least, these statements are too ambiguous to say that Conoco "utterly failed" to raise the issue of the arbitrator's power to decide arbitrability.

Further, Rock-Tenn and Cleveland Electric are difficult to reconcile with the Supreme Court's holding in First Options. Both cases found a party's failure to object to the arbitrator's authority to decide arbitrability conclusive in finding a clear and unmistakable intent to arbitrate. As with USW's argument, this analysis flips the burden of proof on its head, requiring the objecting party to have made some affirmative showing that it does not wish to be bound — which is the natural state absent an arbitration agreement — rather than requiring clear and unmistakable proof of an affirmative agreement to arbitrate. As the Court stated in First Options, "given the principle that a party can be forced to arbitrate only those issues it specifically has agreed to submit to arbitration, one can understand why courts might hesitate to interpret silence or ambiguity on the `who should decide arbitrability' point as giving the arbitrators that power." 514 U.S. at 945, 115 S.Ct. 1920. Further, allowing the absence of an objection to constitute "clear and unmistakable" agreement risks undermining the arbitration system, as "[t]he willingness of parties to enter into agreements that provide for arbitration of specified disputes would be `drastically reduced[]' ... if a labor arbitrator had the `power to determine his own jurisdiction.'" AT & T Techs., Inc. v. Comm. Workers of Am., 475 U.S. 643, 651, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986).

Conoco consistently objected to the jurisdiction of the arbitrator to arbitrate Buller's discharge, going so far as to object to its power over "anything more than just what the Contract says" and "anything else" besides the chain of custody. USW must bear the burden of demonstrating Conoco's "clear and unmistakable" intent to be bound by the arbitrator's decision on arbitrability. Because silence, ambiguity, and merely arguing the arbitrability issue to the arbitrator are insufficient to meet this burden, we affirm the district court's judgment that Conoco did not clearly and unmistakably agree to arbitrate arbitrability.

II. Did the district court err in determining that Buller's discharge was not arbitrable under the arbitration agreement?

Having found that the parties vested power to decide arbitrability in the courts, the district court then had to determine whether the dispute was arbitrable under the CBA. It "vacate[d] the arbitration and the result of the arbitration" and granted summary judgment in favor of Conoco.

USW has failed to challenge the district court's determination that the dispute was not arbitrable on appeal. Rather than argue that the district court's interpretation of the arbitrability agreement was in error, USW argues that the district court failed to defer to the arbitrator's decision on arbitrability.1 But Conoco did not agree to arbitrate arbitrability, which places the question of "whether the dispute is arbitrable" solely in the hands of the district court. The district court owed no deference to the arbitrator in answering that question, and USW does not challenge the merits of the district court's de novo review of that question. And although Conoco dedicated the entire opening section of its response brief to a defense of the district court's de novo interpretation of the arbitration agreement, USW again failed to address that argument in its reply, relying again on the deference allegedly owed to the arbitrator.

Because USW does not cite the district court's interpretation of the arbitration agreement as being in error on appeal, and has not briefed how the district court's interpretation itself — rather than its lack of deference — was in error, these issues are deemed abandoned. Hobbs v. Blackburn, 752 F.2d 1079, 1083 (5th Cir.1985) ("[T]hese matters have not been cited as error on appeal and have not been briefed. In accordance with a long-standing rule in this circuit, these issues are deemed abandoned."). We affirm the district court's determination that Buller's discharge was not arbitrable under the CBA and its decision to vacate the arbitration award.

CONCLUSION

For the foregoing reasons, we AFFIRM the judgment of the district court.