Source? Do you mean because they can wield larger weapons? In the MM, the centaur has a pike, but there's nothing to imply it can use it one-handed. Am I missing something?
Weapons wielded by large humanoids (like ogres, Minotaurs, trolls, giants ect) are large weapons with increased damage die.
This doesn't apply to any centaurs but they were listing out the problems with large sized pcs in general, not in specific.