I think it springs out of the belief that everyone is capable of being a contributor/earner in our society and giving them something for free, paid by the tax payers, encourages them to be free loaders & is akin to stealing. Not saying it makes sense to me but that's what I've seen expressed numerous times.
Just another myopic view of a given thing. Instead of seeing what is really there or what a given program is really about. let's black & white / good or bad everything and put it into one box or the other. The Republican ability to sell every contributor/earner paying into a pool that supports every other other contributor/earner with healthcare needs as bad has been astonishing. They've literally been doing it for at least half a century.
And forget about it being a foundation to preventive medicine. If everyone has free (or at least "affordable") healthcare, everyone should go to the doctor regularly. No worrying about the cost of checkups and sick visits, you just go. With anywhere from a small to MASSIVE financial roadblock removed, patients and physicians can work on maintaining health and working towards helping patients prevent high cost illnesses like heart disease, diabetes, minimize the risks of cancers (depending upon the type).
Preventive medicine should be one of the foundations of any healthcare system. But the GOP doesn't want the government regulating anything. So when it is suggested (in discussion or via bills) that we tax junk food, fast food, soda, fatty foods, and other foods known to be a regular part of the diets of that are known to contribute to heart disease, diabetes, and cancer to help offset the costs associated with providing reactionary healthcare to the people that consume it (it's inevitable), it's "over-regulation!", "preventing freedom of choice", "the government getting too involved in personal life choices!", etc. And that leads to the obvious hypocrisy related to women's and gender health issues that the GOP is all over regulated or, more precisely, eliminating.
The GOP is all about throwing out a tub full of babies to get rid of dirty bath water. They are so much more in the pocket of the health insurance folks that it's literally been a conflict of interest for decades. And the health insurance big picture is not about prevention and curing diseases...it's ideally (to the CEOs and such) about profiting off of the management of chronic diseases. So, they love heart disease, diabetes, treatable/beatable cancers (because they'll likely come back). Any form of socialized medicine cuts into the insane profits of the healthcare business...and the people that make the real $$$ off of that aren't interested in providing quality care to our nation on the cheap.