Then why are they so strongly against public schools and things like SCHIP?
Because they might feel that the corresponding tax reductions or alternative policy (like school vouchers) and perceived superiority of private schools would make them and their children better off.
Also, a lot of them aren't really opposed to public schools when push comes to shove. That's more of a think tank idea than a grass roots one. This is why Bret Schundler never succeeded in NJ, the suburban folks did not agree with that part of his Jersey City agenda. They're opposed to supporting other people's public schools with their tax money.
