I agree. You shouldn't pay for my kids education.
So who will pay for free healthcare?
The same people that pay for other socialized programs such as rubbish pickup, public schools, public parks, police, fired firghters, ambulance services, prisons, etc etc etc. Even then, if you have HMSA and I have HMSA then we are both paying into a pool of money and I may end up paying for your kids healthcare.
I would personally cut certain other programs to pehy for/help pay for universal health care. Food stamps for starters and some other social programs which don't have the same need and circumstances as health care. I would disolve the VA and Medicare and reogranize it into Medicaid or just start from scratch. A lot of money is wasted in having veteran care separate from regular health care systems. My first priority would be to figure out how to make health care cheaper, then we figure out how to get it to all.
But here again, you are paying for other people's healthcare when you go to a hospital because they have to spread the costs of the patients who are unable to afford the bill. Don't forget that there are social benefits to various social programs that are not directly seen.