We should all demand better public schools, whether we have children in them or not. We should demand that we get our money's worth and we should demand that they not teach inappropriate material. But that all has nothing to do with a parent's decision on where to send his child. The former is a public political problem. The latter is about choosing what is best for one's own family.
As far as the option of private or parochial education not being available to all, pretty much every private or parochial school has tuition assistance for for the indigent. If you have too much money to qualify for such programs, it's a matter of priorities. A lot of parents who "can't afford it" seem to be able to afford a lot of other nice things. They just choose these things over the well-being of their own children.
Let's get rid of the public "schools" altogether. Why should we pay one more dollar for abject failure?