I'm not sure what the issue is with socialized medicine. It might be a bunch of things, ranging from thinking the gov't can't afford it (I have genuinely no idea) to conflating socialism with national socialism (Nazism).

I suspect part of the resistance has to do with fearing government interference with educational and health care decisions, socialized anything interfering with the American mythology about ourselves that we are independent and can "pull ourselves up by our bootstraps" without help. and a tiny bit of resentment that someone might get something for free. All IMHO, of course.