Sorry to ask, I don’t want to seem ignorant but I really don’t get it. Like, I saw a post on someone identifying as Norwegian-American and I thought of what another commenter said that most people don’t do the stuff Americans do and how most people will see them as American. But I see many Americans strongly identify with a culture they were raised with. Is it still okay for them to do that? What’s the point?
Regarding those from “The Old World” this phenomenon isn’t unique to the USA. Most other countries in the Americas, Australia, New Zealand, and South Africa exhibit tying ancestry to not being of the land since time immemorial. It just happens to be that Americans tend to produce the most cultural discussion about it in volume, especially in the English language.
The big thing is recognizing that the culture of the land doesn’t match the culture of your “people”. It can be tough to reconcile that, especially if someone is from a mix of different origins.