That's basically what subsidized or single payer healthcare is, using tax money to pay for it. All you're really saying is that taking money from people to pay for something else is a violation of liberty, so therefor shouldn't every single thing that's subsidized or managed by the US or state govt in some way be a violation of liberty? By that argument we should return the govt and our living standards back to the days of the 1800s.
People can't really explain why it's bad, just that it is bad. So much of the right wing rhetoric tells people what to hate, not why to hate it. Other than of course "PAYING FOR OTHER PEOPLE'S STUFF IS BAD!"