I hear people calling themselves "proud product of public schools" or "a public school guy" a lot. These people reminded me of a dialogue I had with one of my Indian classmates. I asked him what he thought about inter-caste marriages in India. He said, "I don't mind." He didn't approve or disapprove. He just didn't mind. He is from the priestly caste. Think for a second about the way he answered the question.
So they have a choice. They could have stayed in their caste, but don't mind marrying someone "lower" than them. They could have gone to a private school, but chose to be a public school guy. That's self-consciously proud, but also sub-consciously condescending to people who don't have a choice.