Here is an excellent video regarding how NZ (and some other countries) refuse to issue licenses to people to own a firearm if they say they would use it for "self defense."
"Self-defense" is not a valid purpose to own one. It doesn't mean you're banned from using it in self-defense if a situation required it.
I would bet that in New Zealand you're not allowed to carry around any type of item whatsoever if you are carrying it specifically for the purpose of self-defense. But you would be allowed to use an item you are carrying for another legitimate purpose, in self-defense, if need be.
Laws like this are pretty common across the world.