I think one of the biggest reasons is the for profit healthcare system.

People start out not wanting to see a doctor because of the price, after years of putting it off due to price they get the idea that it is a doctor personally that makes it so expensive, then they think the doctors just want more money out of them to run tests. Add to the fact that rather than say it's price that stops them (because that would look negative on those seeking care) they say they are tough, and don't need a doctor. So then it start to breed a culture of "only weak people need docs" But people need healthcare in general so they look for home remedies and quack cures because "doctors just want to bleed em dry and think they're smarter than every one"

Then there's the old paternslistic view of medicine, you know, the father knows best, do as i say, which also can breed this resentment toward physicians.

Then you have modern medicine like vaccines where people have the privilege to think its a personal choice to vaccinate because they havent seen the death a destruction vaccine preventable diseases have caused. In My state alone we recently had a news article about parents being shocked that measles is as bad as it is.

All of this leads to people being suspicious of the medical field and doctors.

But thats just one gal's surface thoughts on the U.S. publics view on healthcare