Sounds like you move in circles where that’s a norm and have decided to ascribe that to private education.
I don’t know anyone privately educated that has those issues, including me and DH. I don’t know anyone who sends their child private who thinks they’re any more special than any other child - simply that they want the best that they personally can give their child, whether that’s a decent home, holidays, opportunities, health care, good food on the table - or the best education that they can access.
You sound like the kind of person who thinks every private school is Eton and every privately educated person is Boris Johnson. Ignorant. And, in your case, spiteful and vindictive. As you’ve shown again.