Back in the 1960s and 70s, when libertarianism was a newly emerging ideology, many libertarians used the term “non-aggression axiom,” rather than the now more common “non-aggression principle” (NAP). This was not just a terminological issue, but also had an important practical implication: Many libertarians back then saw (and may still do see) the NAP as an axiom, rather than as a claim to be established.
Axioms are foundational presupposition on which our arguments rest. By its very nature, a well-chosen axiom cannot be proven (if it can be proven based on your other axioms, the axiom is redundant). Thus, if you’re arguing based on the non-aggression axiom, your interlocutor can simply dismiss your whole argument by rejecting your axiom, and at that point there is nothing you can do except abandon the approach of treating the NAP as an axiom.
There is nothing obvious about the NAP and there is no reason why a sensible non-libertarian should just grant you this principle. Of course most people will happily go along with a weaker version of the NAP, namely that aggression against person and property are usually bad and should usually not be allowed. However, there are many other important values besides non-aggression, and it is not at all obvious why preventing aggression should trump all other concerns.
Trying to base your case for libertarianism on the NAP is essentially just begging the question. A more reasonable approach is to start with premises most people actually agree with, such as the weak NAP outlined above. Then the real job of argumentation begins and only at the end do you emerge with the NAP as the result of a long chain of reasoning. I have sketched some of these arguments in my four-part series on why I’m a libertarian (Part 1, Part 2, Part 3, Part 4). Actually convincing people is very difficult and there are no guarantees of success, no matter how brilliant your arguments, but with this approach there is at least the chance of changing a reasonable person’s mind.