> And black identity is detached from black supremacist ideology?

Yes, it is. Both exist (well, at least black identity and black nationalism do, and that's close enough that I'm not going to quibble about it), but while black nationalism depends on black identity black identity exists and thrives outside of it (and historically does so as a reaction against White anti-Black racist actions and ideology), while White racial identity as opposed to ethnic identities largely does not exist outside of White racism (of which it is also a product, though not, obviously, a reaction against.)

> In fact, logic is useful in evaluating the world.

Logic is useful for evaluating the relationship between abstract concepts, but is only useful for evaluating the world when you join it with all the relevant facts about the world. When you reason about abstractions without facts, or in ways which implicitly make counterfactual assumptions, you reach conclusions that are either without material relevance or incorrect.