To me, the word “libertarian” is very misunderstood in modern times.
However, I don’t claim to know the full history of the word, or what it’s “proper meaning” should be.
I just know that if a common individual even knows what the word libertarian means, it usually gets thrown in a basket with “conservative”, “right leaning”, “an ideology for dirty capitalists” (or something along those lines.
If someone has a surface level understanding of libertarianism they might instead throw it in a basket with “everything goes”, “no rules”, “do whatever you want” (or something along those lines).
After reading Rothbard, my understanding is that the libertarian is the person who stands for individual freedom and liberty above all else, and at every avenue of choice, chooses liberty.
Natural rights must always still be upheld, so the notion that there are no rules at all is nonsense. There are rules, they just apply equally to everyone as they should, they are logically sound / rigorous, and in my opinion easier to understand for everyone.
The claim that libertarianism falls into “the right” is null because it doesn’t stand for any political ideology. It instead consistently selects freedom at every avenue; societal freedom and economic freedom alike.
That’s probably the best I can do for now - hopefully I am closer to Mill’s “On Liberty” than I am further away.