If you are a Libertarian and hold liberty as your core value, why do you not believe in universal healthcare? Nothing impacts liberty more than sickness and death.
I would clarify this to say that it's not healthcare being provided to the populace that violates the NAP, but, instead, the taxes that must be raised to fund it.
It's not the idea of healthcare being provided to everybody that's the issue for libertarians. Generally, the issue revolves around how funds are raised for the healthcare. Namely, taxes.
The relationship between libertarianism and taxes is rather complex, imo. The main issue with taxes that a libertarian would have typically revolves around the interpretation of the NAP. It could be argued that the enforcement of taxes is an aggression that has not been consented to, so, since a libertarian is more in favor of negative liberties, they would take the position that they want freedom from being compelled to pay them. Do note that, like many things, there is a spectrum of this belief — not all libertarians completely oppose taxes. Many libertarians recognize that some amount of taxation is necessary for a properly functioning society. What is essentially universal among libertarians, however, is the minimization of taxes.
I think we seem to have different understandings of what "libertarian" means. I think that libertarian is simply the opposite of authoritarian and has little to do with taxes or other economic stuff.
I think we seem to have different understandings of what “libertarian” means.
From my experience, it certainly feels common that people tend to have different definitions and/or misunderstandings of libertarianism.
I think that libertarian is simply the opposite of authoritarian
I take issue with the usage of the word "simply" — I advise against such types of reductionism. That being said, the comparison gets kind of tricky when one considers the different variants/offshoots of libertarianism, or other freedom/liberty oriented political philosophies. It's tempting to try and reduce political philosophies to a point on a 2D plane, like the political compass, or, worse, a 1D line, like the left/right dichotomy, but it's often quite a bit more complex — thinking in terms of absolute "opposites" can lead one down the wrong path. That being said, without being overly pedantic, libertarianism can be thought of as in opposition to authoritarianism.
little to do with taxes or other economic stuff.
While it may be possible that a definition of libertarianism doesn't directly reference economic topics, they still arise as a dependency or result. Economics and politics are often tightly intertwined.