Because it's socialism and/or communism! I kid, it's not; depending on the type of model and even then, the direction of the model itself. It can't be the latter though, it's certainly not communism.
Using a point that's totally non-demagogic: there are some major budgeting issues in the USA, coupled with the extra expense of a universal healthcare plan that wouldn't be too dandy at the moment. Government debt is no small thing, though not the end of the world itself, still poses a danger to the stability of the social sphere and the political sphere. We should aim to keep government debt to a minimum ideally, and reduce it now, whilst we can - adding the subsidies that typically go with a universal healthcare plan will cause more expense.
Some may oppose it for ideological reasons, do I want to pay for someone who clearly, is being an absolute arse and injuring himself all the time? No, for a conservative perspective, he should take more personal responsibility for his own healthcare provisions and be a tad more careful, I shouldn't have to pay for it if his silliness leads to using up medical resources that I have to contribute towards involuntarily.
Some are more market orientated and believe that if we take away the legal restrictions already on healthcare companies in the USA, like that whole deal with buying along state borders (I don't even know this one), the market will force the less optimal or negligent companies out of business, as in the market (presupposing rationality), no buyer would choose a negligent or downright unethical (deceptive, etc) insurance company over one that functions smoothly as to do so, is absolute irrationality. There's also the question of "will universal healthcare dilute the quality of care?" that I guess one could link in with this point about the market's function in healthcare, namely, if we're having a totally public model as opposed to something that utilizes private finance and resources which are often perceived as superior in quality to the former.
Some may just have complaints with the government, whether it be an ethical complain (big government = bad) or a complaint based on the historical evidence that undermines the USA's bureaucracy/executive's competence in running ventures that they have undertaken, mainly, that they can't keep out of the red.
I'm no conservative, but those are some potential reasons. I've lived in a country with universal healthcare for all my life, I've honestly never had a problem with it, however, I can understand the reasons given by American conservatives on why they may dislike the idea. So yeah, here's some reasons I often see around here, I don't really care about the issue as long as someone doesn't make a totally demagogic statement or makes false claims about universal healthcare itself.
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