It's a false dichotomy. Identifying as biracial (which is a term I actually don't like personally because there are lots of us - especially in the African diaspora - with much more complex genetic/ ethnic histories than just black/white) includes both. Just factually, having one white parent and one black parent means you have the heritage from both. From an internal perspective it really is as simple as that for a lot of people (including myself).

How society treats you is a different kettle of fish. I always think that it's interesting that people seem to expect mixed people to identify with the side that isn't white to the exclusion of their (/our) whiteness. You can't have it both ways. You can't critique biracial people for "not being black enough" or having colourist privilege and then get upset when their whiteness is acknowledged. Identifying as both (and, separately, neither) makes sense because we constantly have different identities thrust upon us depending on the context of our surroundings.

Hope that gives some context to the piece, which I also really enjoyed :)