It's kind of amazing - friends of mine consider private school (which cost as much as a college education when I was young) to be a must-have. Imagine paying 20-40k a year for your kid's high school, or sometimes grade school! And these are very successful people who went to public school themselves. One is a college flunk-out.
My wife and I don't have kids, so I guess I don't get it. I suspect it's not just about education, but also classism, trying to ensure the kids end up in the right socio-economic class when they grow up.
Maybe at the very elite end, but I don't think that applies generally. No one's going to Catholic School (IIRC, the biggest single type of private school in the US) because of "who you grow up knowing," for instance.
...
but at least in my local area those two things overlap nigh-identically.