By the same token, anyone whose child is not registered in the school shouldn't have to pay to support it.
And by that same token, anyone that does not have children at all shouldn't have to support it either. Then what you have is people paying for their own children's education. If this is to be the case, then why pay taxes at all? Cut out the middleman.
The real problem here is that many people truly cannot afford to pay for their children's education. Which brings up the point of "why are they having children if they can't afford it", and opens another huge can of worms.