Because FREEDUMB! and DEATH PANELS! and socalislists and stuff.
Seriously, it really is absolutely insane. And the idea that our system is just fine and is superior to every other heath care system in the developed world is equally insane.
I had to switch doctors because my old doctor gave up my health insurance because they were a pain to deal with. And I couldn't afford to see her without the insurance so I was forced to switch doctors. Where was my freedom of choice there? I liked my old doctor! (fortunately my new one is also pretty good). We switched pharmacies not because we wanted to but because out insurance company told us we had to. Where was our freedom of choice there? And we dare not switch insurance companies because my wife has per-existing conditions. Where is our freedom of choice there? The idea that somehow people with single payer/socialized medicine/whatever you want to call it, have less freedom of choice in their medical care than we do with our current system is not grounded in any reality.
Especially as many in UHC countries also have private insurance - for increased convenience as opposed to necessity.