It's subsidized. Medicare is currently costing taxpayers over $350 billion a year. Premiums "paid for it" amount to about 1/10 that amount. That's a handout.
And as one of those taxpayers, I am most certainly paying for it anyway.
I'm certainly in favor of abolishing medicare and social security as long as I can get my previously-confiscated premiums (and those paid on my behalf by my employer) back, with interest.
None of this would be a problem if these programs were voluntary and self-sustaining entities.