And yet I all but guarantee that anyone who has ever said "black people can't be racist" did not actually mean "black people cannot be discriminatory, racially prejudiced bigots." (I'll allow for corner cases where people are idiots - because that happens with anything.)
Anyone at all can plainly see that nothing stops black people from being those things.
So the singular reason to get upset when someone says "black people can't be racist" is a failure to recognize (and based on this discussion I'm pretty sure it's a choice for many) the scholarly definition.