"Nationality" and "ethnicity" are different things. Americans can also be African-American, Chinese-American, etc etc.

You don't have to call yourself Pakeha (although the dribbling bullshit about it being like the N word does nobody any favours. It is nothing like the N word and is not used as an insult but as a descriptor) but New Zealander isn't an ethnicity and trying to make it be one ranges from being pointlessly dumb to being racist.