There's no inherent conflict between rich people having better stuff and equal rights. For better or for worse, the American belief on this subject is that opportunity to better one's economic situation should be equal, but that it's fair for quality of life to be dependent on some amount of success in taking these opportunities.
That aside, though, I think the point is that any reasonable person with kids will do whatever they can to bring them up in the best way possible, with whatever resources they have. Maybe the US public school system is poorly executed but well-intentioned; maybe it is not even that. It doesn't matter; it is what it is. There's no shame in not participating in it if you have a choice (participation is not what it's short on!). Maybe we will have amazing education for every US child one day, but who knows when or what form that will take, or what will drive it. Private school may be a luxury, but you don't have to be rich to home-school, it's a valid and attractive option for many parents in areas that are cheap to live in but have terrible schools.
I disagree with that pretty strongly - if you have time, go and read the NYTimes link that I posted below.
Their point is that many children don't have that opportunity, since they're already well behind by the time that they start school. And a large part of the difference in school performance can be explained by differences in the students economic background and family life.
This doesn't square with the equal opportunity / everyone's equal that the US seems to be so fond of.
I agree that "equal opportunities" is a myth. People grow up with vast differences in the advantages they've been given.
However, deserving equal things doesn't mean you get equal things. See the fact that people have different amounts of money from each other, and have for thousands of years. We celebrate the ability of individuals to better their life situation as much as possible, and we don't shame rich people for spending money to give their kids a better education than the government can provide.
The US public school system is simply an attempt to give all children in the entire country access to some education. It would be great if it was a gleaming example of delivering quality on a large scale, up to the standard of, say, McDonald's, but alas it is not.
That aside, though, I think the point is that any reasonable person with kids will do whatever they can to bring them up in the best way possible, with whatever resources they have. Maybe the US public school system is poorly executed but well-intentioned; maybe it is not even that. It doesn't matter; it is what it is. There's no shame in not participating in it if you have a choice (participation is not what it's short on!). Maybe we will have amazing education for every US child one day, but who knows when or what form that will take, or what will drive it. Private school may be a luxury, but you don't have to be rich to home-school, it's a valid and attractive option for many parents in areas that are cheap to live in but have terrible schools.