That's clearly not how it works. Kids who drop out of primary/secondary education don't get to pay lower taxes in adulthood. Taxes pay for current spending, and the taxes you pay are in return for living in a society.
This is too literal a view of the world that doesn't help progress the discussion. Obviously no child pays for exactly the chair they sat on in the classroom, or the piece of chalk they used to write on a blackboard, or whatever they use in classrooms these days.
When I say "you pay for your own schooling through taxes" I'm saying that most countries have tax systems where citizens contribute according to their earnings / net-worth, a share of the costs of running all of the parts of society that aren't privately owned - or some approximation of this idea.
This means that if you're paying your taxes, the implication is that you're paying "your share" of running education for society and someone did that for you when you were a kid. Maybe you're paying for iPads in 2022 for other people's kids where you only had chalk, but some other schmucks also paid the doctors salary (unless you're in the US I guess? not sure how that works there) that delivered your birth and nobody expected you to hand over a dollar bill as a newborn to pay for yourself.
But that's exactly the distinction that matters. Treating the services one has received as a debt implies that one must pay back that debt and is free of any other obligation. In reality, as you're pointing out, we're all contributing to the current and future wellbeing of each other, and we all benefited from others' contributions in the past.
Pay-it-back vs. invest/pay-it-forward have quite different political implications, and the fact that society does and always has been in pay-it-forward mode gives lie to the earlier commenter's claim that subsidies are slow but fatal.