"Our system" is a hodgepodge of different systems. We've got regular system that most people are on (private hospitals, private insurance). We've got MediCare (private hospitals, public insurance). And we've got the veterans system (public hospitals, public insurance).
If a medical care system that even touches public money is so bad, then why do we have systems like that? Why is 'socialism' some sort of political hot-potato when we have so many current social programs that no one wants to give up that qualify as 'socialism?'
Because rhetoric has nothing to do with truth. We soaked generations of Americans in the idea that 'socialism' = 'communism' = 'Russia' and 'China' = 'The Bad Guys'. That creates emotional responses on part of a large segment of the population whenever you assert something is "socialist" and good luck trying to reason with someone in the middle of an emotional response.
So convincing the voting public that something is "socialism" skews public support, and thereby the inevitable compromise, more toward your private benefactors.
The disconnect between rhetoric and objective reality is how we've managed to create a society where people at Tea Party rallies can emphatically demand that the very government that can do no right and needs to be largely dismantled in their eyes, needs to leave their social security, medicare and military alone.
If a medical care system that even touches public money is so bad, then why do we have systems like that? Why is 'socialism' some sort of political hot-potato when we have so many current social programs that no one wants to give up that qualify as 'socialism?'