Primarily, because universal healthcare involves greater government expenditure and complexity, and Republicans consider both the extra cost and regulation an assault on capitalism and states' rights. This is the party which is politically beholden to a man who famously said he wanted to shrink government down to the size that it can be drowned in a bathtub[1], after all.
Also, because it smacks of socialism, and socialism is considered a moral evil that creates an underclass of lazy underachievers who don't understand the dignity of a hard day's work and only want to feed at the government trough. And of course by implication vote for the other party.
It's probably also worth pointing out that it being the way things are done in Europe and elsewhere only makes it even more offensive, because Republicans believe in American exceptionalism - which implies at its core that our way is Just Better, and everyone else is Just Worse.
Also, because it smacks of socialism, and socialism is considered a moral evil that creates an underclass of lazy underachievers who don't understand the dignity of a hard day's work and only want to feed at the government trough. And of course by implication vote for the other party.
It's probably also worth pointing out that it being the way things are done in Europe and elsewhere only makes it even more offensive, because Republicans believe in American exceptionalism - which implies at its core that our way is Just Better, and everyone else is Just Worse.
[1]https://en.wikiquote.org/wiki/Grover_Norquist
tldr; money, politics and xenophobia.