OK, firstly sorry, this is a lot longer than I thought it would be and possibly outing. But first time I have actually had the guts to say something on this subject.
I'm still trying to work out if non binary is just the new name for gender non conforming where gender is just stereotypical behaviour.
I have always been gender non conforming, a tom boy from birth, my family nick name was Butch. Did not have many female friends as a child. Always played with the boys, ignored by the girls as "weird," embarrassment to my very traditional mother. " Why couldn't I be like all the other girls!!!!"
Best subjects math and science but also drama ( always given male or the adult roles in all school plays or musicals, as was adult height and build at 11/12 but playing teen/adult female roles in amateur dramatics outside of school during the same period ) & art. Dyslexic but not spotted until I was an adult because..... well I was a girl and in the top set for everything. But you know what. THANK GOD I grew up in the 70s and 80s.
Joined the WRAF after A levels, but was seriously injured in a freak accident during training and had to leave. Ended up in the banking sector for over 15 years. Only full time, working mother in a team of 70 stockbrokers. (Whole other story on sexism in the workplace, but for another day, hey!)
Now I have always liked the alternative boys, loved long hair and makeup on men ( giving away my age here). DH ( and best man) had longer hair, more jewellery and make up on than me at our wedding.
Dh ended up as SAHD, we started off both working part time around the 3 kids, but I could earn a lot more than him, so why not have one of us at home with the kids. He did work part time around me and the kids so we'd have extra money for Xmas or holidays or just to escape the 3 mini monsters for a while . 
My view female/male is simply words we have applied to Sexual dimorphism species.
Woman is female of the human species. Just like doe, vixen or ewe is the word we have given to describe a female deer, fox and sheep.
Everything else is just personality, abilities, personal traits and society's pigeonholes.
Sorry this is so long, but final thought, looking at the female names for mammals, god they seem so depressingly sexist. Or is it, that so many are used as an insult? Really not the same for the male versions. Funny that!