You're still missing the point the parent was making.
"it seems like you are missing the point: in a pervasivly racist society, discriminatory behaviors creep in the subconscious of everyone, black/white/antiracist/whatever, and we have to consciously struggle with them."
?
I have recently argued against my own misunderstanding of someones explaination and find that embarrassing so I am actually listening.
We all hold prejudices that we all need to be mindful of. Getting tangled in the weeds of arguing about semantics completely derails that point.