"same chances to get well when sick"

Your desire for health equality must come at the expense of political equality

Some are allowed to tax others, but not the other way around

Moreover, how do you think this all worked prior to state intervention in healthcare? I happen to know that in the early 1900s Americans worked 5 days per year on average to pay for healthcare, and now it is over 50.

Perhaps you are ignorant of the history of mutual aid societies, doctors providing free or discounted care to the indigent, and religious/charitable provision of care (notice how many hospitals are named "Saint so-and-so").