You are missing the key feature: solidarity.

It is not paying for your own medical care it is paying a small proportion of everyone's medical care.

And in fact for a proportion of the population it is in fact free or nearly so because they have never paid any income tax or the cost was so high that the taxes they did pay plus the proceeds of selling very possession they had and selling their children into servitude still wasn't enough to pay for it.

And lastly, we all understand the point of taxation and redistribution (at least in Europe we do) so what exactly was the point you were repeatedly failing to make clear?