It may be that they lack perspective on themselves. The kind of humility that comes from the liberal education you described is the kind that comes from putting yourself in perspective. Our problem in America isn't so much the pride of an individual person(although that can be a problem too, as Bill Clinton, and before him the likes of Aaron Burr, demonstrated), as it is the general lack of perspective on the part of politicians and citizens. People aren't usually exposed to thoughts and history that aren't from the recent past, if that.
You're right about the study of the classics. An educated citizen or statesman ought to know the Greek and Latin classics, plus the writings of the Founding Fathers and authors like Bastiat, and other modern classics.