Full-on anarchism, or anarcho-capitalism, ok, that's a hard sell.
Libertarianism? It's basically "never initiate aggression" and "live and let live". That's about it. I don't know what's extreme about that.
You don't? Live and let live means, in practice, let die. Libertarianism says, if you had bad luck and are poor and you get a disease you can't pay to cure, you die.
Libertarianism is the extreme of selfishness. "Live and let live" means "I've got no obligation to anybody else, screw 'em." In modern society, that's incredibly extreme.
What libertarians are against is coercion and force. They don't want to be forced to do what somebody else thinks is morally proper, in most cases for yet another person. That way lies tyranny.
The concept of selfishness in the libertarian sense is "put your own oxygen mask on first before helping others".
Most libertarians are pretty generous givers in terms of both charity, emotional support, helping hands and community. They just dislike having a gun to their heads to be that way.
There's just no plausible evidence that people in general are charitable enough to fund all the necessary hospitals and schools and so on that society requires. It's just not human nature.
So to the children who will go uneducated and die of sickness, that insufficient charity isn't going to mean much.
I don't follow your logic.
The non-aggression principle is what's at the core of libertarianism. It's to never initiate violence against peaceful people.
Helping others voluntarily is certainly in keeping with the philosophy.
> Libertarianism says, if you had bad luck and are poor and you get a disease you can't pay to cure, you die.
No it doesn't. It says we're going to help that person who is poor or in need, but we're doing it voluntarily.
Experience shows that not only is voluntary assistance deeply insufficient, but that it's also often extremely biased and prejudiced.