But there’s the is-ought problem: We know what the nature of man is but which rights/laws ought there to be?
The Natural Law tradition from which Rothbard derives his version of the NAP rejects the “is/ought” question for reasons too extensive to go into here (but I recommend, for example, Ed Feser’s Aquinas or The Last Superstition; he may be a lapsed Libertarian but he’s still a decent philosopher on things like that. Also books by David Oldenberg such as Moral Theory. I’m also sure if you got in touch with David Gordon he’d be able to recommend works that address the so-called “is/ought problem” and attempt to refute it). (N.B. Aquinas was not “just” a very significant theologian; he was also a very significant ethicist that even non-Catholics, like myself, and non-Christians, can and should take seriously. That is to say, he makes points that can and should be considered separately from his purely religious arguments; Rothbard definitely wasn’t a Catholic but took him, and all the Scholastics, seriously. I point that out because I know there are a lot of Athiest libertarians, and I don’t want them to feel they’re being confronted with a religious argument that has no bearing for them).
In short, an acorn is a seed of an oak, it is in its nature to sprout and grow into a study, healthy oak tree, and a good acorn will – and ought, by its nature – to do that (good acorns also serve to feed squirrels, and healthy acorns will, if eaten by such squirrels, produce healthy squirrels); any acorn that falls short of that is deficient in some respect; it’s not as good as it could be.
A good square has four sides of equal length, each one at a 90 degree angle to two others and perfectly parallel to the line opposite it. Any square that does not meet this standard (as all real squares fail to do) is deficient in some respect, not quite as good as it could be (which does not mean they aren’t good enough).
From that one goes to humanity; humans have certain qualities, and the word humanity is used advisedly here because it is an English word that still retains its pre-Humean unity; humanity not only designates a type of being (humans); it also conveys a sense of how they ought to behave (humanely). Is and ought are a unity in this moral conception, and the discussion/dispute then is over what constitutes the good for humanity, what humans should do if they are to pursue their nature.
Note the above is a short, imperfect exposition of the principle, into which many holes can be poked, I therefore recommend any of the above resources for more fully addressing it.