The property taxes = education bit is quite US-specific, but still -- property taxes are paid by the people with the most property -- not the ones with the most children. (Outside the US from what I've seen education is not normally linked to property taxes).
But the same argument holds true; if you assume your parents are paying for you with the money they put in, are you sure they paid their own
If your parents paid enough in taxes to cover your education (and assuming someone else in turn funded their "public" education, etc.), that's obviously not always the case. I should add that government services for children (like daycare and significant tax breaks to parents, in France) can be much more significant than in the US.
Children's healthcare is another thing that's not used in proportion to how it's paid -- there's a chunk of the population whose kids will only ever need a few jabs and stitches now and then (so those kids don't "owe" much). Then there are a few kids who will require thousands or millions of dollars worth of care -- including special schooling, etc., not just direct healthcare, and the problems they have may mean they will never contribute anything back.
That gets at the whole point of all this -- yes, of course some people pay more than they consume, because these are services intended to make life more fair. Imagine if your parents didn't pay enough property taxes to fund your schooling, so you didn't get to go. Or if you have a child with severe disabilities, and you have to leave your job to care for them and build every ramp you need by yourself (or mortgage your house to pay for medical treatment).
If the people who would otherwise be covering the difference all stop paying once they've covered their own services, that leaves a heavier burden on the people left. If enough of the lucky ones check out, services-for-all simply disappear.