Hopefully you can see that I'm not making "the biological argument" you probably had in mind, i.e. a biological essentialist account of gender. The biology totally supports non-binary people, and in fact the current evidence is that brain sex is largely "non-binary", with very few people having brains that fit into binary boxes.

EDIT: https://pmc.ncbi.nlm.nih.gov/articles/PMC4687544/

Our study demonstrates that although there are sex/gender differences in brain structure, brains do not fall into two classes, one typical of males and the other typical of females, nor are they aligned along a “male brain–female brain” continuum. Rather, even when considering only the small group of brain features that show the largest sex/gender differences, each brain is a unique mosaic of features, some of which may be more common in females compared with males, others may be more common in males compared with females, and still others may be common in both females and males.

The lack of internal consistency in human brain and gender characteristics undermines the dimorphic view of human brain and behavior and calls for a shift in our conceptualization of the relations between sex and the brain. Specifically, we should shift from thinking of brains as falling into two classes, one typical of males and the other typical of females, to appreciating the variability of the human brain mosaic.

Only around 1% of brains fit consistently with the binary "male" or "female" characteristics.