Why can't my 13-year-old brother-in-law be a godfather if he's confirmed?
The short answer
Confirmation isn't the only requirement. Canon law requires a godparent to be at least 16, unless the bishop sets another age or the minister sees a just reason for an exception. Godparents help form the child in the Christian life, and a 13-year-old is still being formed himself.
The age requirement
Besides confirmation, canon law requires a godparent to be at least 16, unless the bishop has set a different age or the minister of baptism judges there is a just reason for an exception (CIC 874). Your priest apparently has not found such a reason.
Why
Godparents are to help the parents form the child to live a Christian life befitting the baptized and to fulfill the duties of baptism (CIC 872). A 13-year-old is still being formed in the faith and may not be ready to share responsibility for another's spiritual formation.