I think Paul's argument is misleading. I say that as someone who went to both in high school. There are public schools that put out the best of the best (i.e ma

I think Paul's argument is misleading. I say that as someone who went to both in high school. There are public schools that put out the best of the best (i.e magnets and magnet-like schools) and there there are private schools that are just holding pens for the spawns of the wealthy and a few talented athletes. But one thing that many private schools provide that most public schools don't is the academic agency for students to pick from a wide range of courses that match their ability and a standardized curriculum that pairs well with those choice in terms of thoroughness and rigor. Most public high schools don't have AP or IB courses and the ones that do tend to have them in limited supply in the hard sciences ( i.e. AP Physics C, AP Computer Science A, etc). Pursuing some sense of rigor involves taking courses that seem difficult rather than taking them in the hopes of forming a more cohesive understanding for one's future pursuits. Self-teaching obviously helps quite a bit, but that doesn't aid most students in achieving a firm foundation for say, undergraduate research in Physics.