No civilization ever collapsed because the poor had too much to eat.
It's not brain size perse, as it is relative brain size. And even that's deceptive. For instance, as I understand it, most of our large frontal lobe structure has nothing to do with intelligence per se; it's dedicated to the one thing human's excel at: abstraction and imagination. That co evolved with advanced tool use.
Other hunting species may have a broad cranial structure for similar reasons: you have to imagine what the prey might do to anticipate it's moves.
Anyway, brain size by itself and without qualification paints too simplistic a picture.
Be kind to your enemies. It confuses them.