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.
Quora answerers did a better job than me making the point about raising your kids: http://www.quora.com/Education/If-you-send-your-kid-to-priva...