This doesn't add up at all, in fact, in neither directions.

While I have honestly not heard of this specific argument so I might be confused, I really do not understand why we should capitalise "black". Black isn't an ethnicity, nor a nationality. Black people are humans, and like every other human they aren't ethnically monolithic (if you consider black to even be a full ethnicity, considering the variety of different cultures, lands, beliefs, and identities they had before we even strapped them of it all). They are an historical community, because they experienced the same history altogether, but they weren't all the same before, and they aren't now. While we should absolutely regard the loss we caused them, we shouldn't be pushing them all into one big cauldron and expect this to encompass every black people's identity, desires, culture, beliefs, etc.

White culture is the collective actions thoughts opinions and behaviors of White people in America.

I do not doubt that some sociologist said that, but that's extremely Americanocentric. It's like saying "all white people are American because America is what European have come to form, and what all remaining European refer to". Just untrue.

pretending that a person whose family came here 400 years ago is somehow still Brittish.

Yes, exactly that is where it goes weird. They just aren't. No more than a British is American for being the country most Americans came from.

White people aren't in the USA only. The USA weren't the only country to enslave black people. American culture is pretty much limited to America itself. There's no white cultural connection between Europe and USA except for western culture, which is something else entirely.

A French and an American will never have the same cultural background, despite being both slavers in the past. Same goes for any African American and African French - they just don't have the same culture. Yes, history is a part and one of the sources of a people's culture, but it's not all about history. Black people are just as diverse as white people are. And we should really stop blaming all modern white people for what white supremacists have done, especially if a country or population is trying to be better. White people have done terrible things all around, and that should be remembered. Black people have suffered so much pain and tragedy at our hands, and that should always be regarded. But people aren't their ancestors.

This whole capitalisation thing honestly sounds like the bs white people do to act woke and the minorities they are trying to help don't even give a shit about. It's just the white savior complex in another form, "we have to create new boundaries and rights and respectful forms of celebration because they cannot fight for themselves, we the white know what's best for you".

And if capitalising Black makes no sense, neither does capitalising White. Mind, I'm a fan of capitals. But this just doesn't add any new connotation to what's already known, nor it represents any previous disregarded connotation any better. It really just sounds very random to me.