It is not possible to answer your question without more information. What is the basis for his request to modify legal custody? Assuming there is a court order in effect regarding custody, he can ony obtain a change in custody by proving that there has been a material change in circumstances and then, after meeting that burden, by establishing that a change in custody is in the child's best interest. Since joint legal custody requires that you and he make material decisions for your child together, has there been a history of an inability to do so?