There are different justifications for the NAP. Rothbard derives the NAP from natural law and natural rights. He explains this at lenght in the first chapters of Ethics of Liberty. But there’s the is-ought problem: We know what the nature of man is but which rights/laws ought there to be?
Hoppe and Stephan Kinsella have come up with different justifications for the NAP which are described in the articles I linked to.
