I fully support a public education but in the US, the school system is massively overloaded. We blame schools for everything and schools are all too eager to accept responsibility for anything and everything.

School athletics programs paying for huge multimillion dollar stadiums should not be possible. And on that topic, independent school districts should not exist. One state, one school district. https://en.wikipedia.org/wiki/Eagle_Stadium_(Allen,_Texas)

Refund or voucher to the parent suffering it. Still not seeing how you went from that to “don’t you understand that non-parents should fund public schools?” The premise is that those hurt by it, parents, recover money to otherwise educate their kids. Nowhere in that was a claim that the childless should get money back for being childless, so I don’t see how addressing that is responsive.

I think you’re saying that If your kids are not using the service, then you should not pay the tax.

This doesn’t sound any different from someone having no kids, not using the service, and expecting a refund.

No, they're hugely different. One of them accepts that the state should still be paying for education of children regardless of whether your personally have children -- just with better options than failed public schools. Which is why lectures about how "we should all be paying for kids' education" is very unresponsive. Which is why I said so. And have not yet gotten a substantive reply that addresses the criticism.

The majority of private schools are religious. We don't usually let tax money go to religions.

Like Notre Dame and Brigham Young?

I’m still not understanding your point.

I must pay for socialized education regardless if I use the service. I might choose to not use this service because I lack children or I may choose a different provider. But this doesn’t mean I don’t have to pay my taxes if I don’t want to use a gov service.

What makes adults with kids special that they don’t have to pay this tax when they don’t want to use the service?

But I don’t care if their kids use it. They are not funding their child, they are funding the system of public education.

Which vouchers are. Why is this so hard to understand?

No, they aren't. Perhaps you're having trouble telling the difference between people who don't understand your argument and people who disagree with it?