The idea of "whiteness" being good is a super new concept in the grand scheme of things. People like to say things like "Irish and Italians werent considered white", which is not accurate because they've always been considered white.

"White" just wasn't enough to be part of the "in group" and people nowadays dont have any other terminology to describe what the in group was other than just white. If you go back to the early 1800's, the in group was Protestant anglo-americans. That doesnt mean people from other European countries werent white, it just means they werent part of the in group.

"White" being the defining factor of the racist top hierarchy is super new, like 1966 new. The leader of the American Nazi party realized that they could gain more power by folding in white people from outside of their traditional in group (germanic or nordic), so inspired by the black power movement, he coined the term "white power".

Even now, just being white isnt enough to be part of the top category to racists. Maybe an Italian is considered part of the in group, but not middle easterners (who are legally white in the USA).

Since "white" as an identity of people is relatively new (and only really makes sense in a racist framework), a lot of European/Middle Eastern Americans tend not to identify as "white" but instead by whatever jumble of identities their grandparents might have had. If your grandparents tell you they had a Cherokee grandparent, how are you supposed to know any different.