My children's mother is West Indian; I'm mostly Anglo. They both grew up calling themselves biracial, but my daughter now calls herself black for (I think) political reasons. I haven't asked my son how he identifies racially.
I don't agree that we have no choice about going along with the system that classifies people in binary fashion, even if that system continues to dominate in this backward country. I am proud to share the multi-racial heritage of my family, and happy to let each member of that family decide what identity means to them.