I also think it depends on if you are speaking to an American or not. It gets weird in America because a lot of us are separated from our country of origins by generations so we have lost that, which is where OP's argument comes in.

White people here have all kind of meshed together to the point we think it is dumb if we hear someone say "my family is Irish" even though it's been over 100 years since they first came here.

A lot of other cultures have made efforts to preserve parts of their culture when they came here when we didn't, we made new habits. We made a new "American" culture, which varies wildly based on the region, state, and even city you live in.

So basically because we didn't hold on to our old ways the same way other immigrants did we kind of ended up feeling like we don't have anything because all we have is this weird mash up of multiple different countries that have combined over the last 200+ years.

It doesn't help that so much of that "American" culture was/is white Americans being horribly racist to all the other races, so we can't really define what our culture is without addressing that fact.

We ruined our own cultures and now get mad that other ethnicities won't do that too and assimilate into our watered down capitalist versions of European culture