All trolling aside, I'm going to take a stab at the question ("Why be ancap?") from a bit of a different angle for those who haven't really thought of it before.
The angle is this: Respecting human rights (essentially the NAP) is intrinsically moral, which contributes to both society in general and ones sense of well-being and self-esteem.
Also, alongside the general principle of like attracts like, it should generally (leaving aside the tendency of libertarians to be more disagreeable and socially awkward than non-libertarians) lead to an increased tendency to attract other ethical people into ones life, which is a good thing.