It's probably due to legal reasons. If under 18 year olds get status, it means they can enter lounges without an adult and can consume alcohol without supervision.

That's not a good reason to deny minors entry to MPC, but who said the reason had to be good?

Anyway, if a minor is travelling alone in F or J, they will have access to the lounge anyway but I guess there are not many minors who travel solo in premium cabins.

BAEC has the same restriction as MPC, and the folks on the BA board seem to think it's due to the alcohol.

AA probably doesn't do the same because in their lounges, alcohol generally has to be ordered from the bar and they will ID you if you look too young.