Racism is the answer. The original half white, half black or really half white half anything people were products of rape. They weren't acknowledged as half white because their owners/colonizers would've had to acknowledge rape.

On top of that racism would've prevented a biracial person from being seen as being half white because they would've still been subjected to the same treatment as their black counterparts (one drop rule). I mean technically most Black Americans have a considerable amount of European blood (I believe 25-30% is the average), but you'd never call a dark skinned black person with two black parents biracial regardless of the results of a DNA test. You'd call them how you see them.

This is pretty true until this day. Biracial folks experience the same type of racial discrimination as Black people. They will have a mainly Black experience and many of them have decided that because of their experience, they'd prefer to just be called Black. If we were being technical, we'd recognize that race isn't real and no one is really biracial but much of what we consider to be race is just phenotype.