I'm using the word "right" in a very strict constitutional sense since I think at the core it's what we're talking about here.

"Inalienable" and "God-given" rights have less to do with divinity and more to do with very precisely defining what those rights are. A concept of an inalienable right is foundational to the US and the Constitution, so let me see if I can rephrase what I'm getting it.

A right is not something that can be taken away by a person or government; it's not like a parent who lets you stay past your bedtime to watch TV a few times. An inalienable right is something that can't given or taken away (this is an important concept)

In a same way, it cannot be given to you by the government. That's what makes inalienable God-given rights such. Again, don't focus on the religion here, not the point.

A right to free speech, bear arms, assembly - they can be infringed upon (and severely) but they are not really given to you by the government nor can they be taken away by one. Note their ephemeral nature.

Now, with that in mind, think about what health care is. It's a service that is provided to you by other people with their inalienable rights. Hypothetically, if every doctor and nurse refuse to do what they do and just pick up knitting instead, what happens to your "right"? Who will render healthcare for you? Note that you can still use your right to free speech to complain you're bleeding out but so what? You can still bear arms. But if it's your right to healthcare and nobody is willing to (hypothetically) render it, then someone will have to be compelled to do so. When someone is compelled by the government it's a threat of force - how else would you do it?

So again... if your right necessitates someone losing their liberty, then it's not a right, not in a strict sense of what a right is.

The left has done an excellent job of muddying the language (illegal immigrant becomes an undocumented citizen, a violent rioter is a mostly peaceful protestor and any handout is now a right)