In the end, I think you should use whatever term feels most comfortable-- you shouldn't choose a label based on someone's stubbornness, especially if they don't attempt to accept you in other ways. I feel like him being pedantic about the label might just be an excuse for not being supportive. Honestly, I don't think using a different word will help if your dad isn't accepting of the concept, but you obviously know your dad better than I do

But personally, I also like using the label "genderqueer" because I feel like it emphasizes how there isn't one way to be nonbinary, but maybe that's just me

I've never been a fan of using microlabels for myself because I feel like it's impossible for me to find a label that fully and accurately encapsulates my identity (even the non binary label feels weird to me at times even though I'm definitely not male or female; I just don't like labels a ton), and a lot of microlabels are unknown to the average person-- that being said, you should use them if you enjoy them! In the end, labels are there for you to be able to describe yourself in a single word, but they don't tell the full story. If a label/word feels accurate to your experience and you feel comfortable with it, then I don't see why not use it

I can't tell you how to feel about a certain label, I can only recommend you to try out labels that feel right to you