For example, how black identity can exist despite black people consisting of a number of distinct, large population in different countries on different continents, and how white identity doesn't exist despite the same being true for white people.

Its easy to explain using the leftist doctrine. If you don't know the explanation, then you understand how they view race. It's socially constructed. White is the norm, it's the assumed identity. Black is a socially given identity, the outsider and the oppressed. It's something given to so-called blacks by society.

OP is right. Don't engage and just assume your assertions as true.