The rich shouldn't be able to buy their kids a better education.
Why not just improve public education to make it better than private education?
The point is that as long as the rich are allowed to buy their kids a better education, they're going to use that right. You can improve public education all you want, but so long as the rich can opt out of the system, it's going to be at a disadvantage and the wealthy are going to be able to perpetuate income inequality.
I don't really think that's the problem when it comes to income inequality.
I went from an ordinary public high school to an elite east coast university full of prep school kids from Phillips Andover and such. They had no leg up on me in terms of academics. Richies pretty much use private schools so their kids can meet each other and perform a bunch of homoerotic rituals or whatever. If it wasn't high school, rich people would just find some other marker of wealth and importance to waste thousands of dollars on.
Even if all that were true (and its no secret the privately educated dominate), it'd be worthwhile achieving equality in one of the most important aspects of life, and shutting one door in which they're able to perpetuate their privilege.
Equality usually never works by restricting individual freedom. That's ultimately destructive and quickly pisses everyone off. Look at communist societies and how they stultified their culture by attempting that type of forced equality. What I'm saying is that rich kids don't obtain an exceptional educational benefit from these schools. They obtain an exceptional social benefit. That social benefit of being rich is impossible to remove without having a communistic society.
I think you're overgeneralizing private schools. They're not all Choate-Rosemary, you know.
Maybe that's true. I live in a black neighborhood and if I had kids, no way would I send them to school here. If your neighborhood public schools are complete garbage, it's an understandable impulse for parents.