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.