I had that guy at fencing insist I'm German. I'm 1/8 German on 2 sides adding up to only 1/4. He also insisted I call someone who is Asian "Korean," as if I had a chance to know that. I don't like labels like that. I tell people I'm American, and everything else is horseshit, it's my last name, whatever. 1/8 German last name and here the longest. I have 2 sides more recent immigrants from non-German countries and assimilated. I hear stories of my great-grandfather chastising his own wife for not speaking English enough, but I also read (and I got ahold of these more recently) newspaper articles and eulogies of him and how much he loved America. He actually only came for a visit for one summer but he loved it here, and stayed, and found a wife here who had come with her family from the same country. This in contrast to my other great-grandfather who went back to his village (on a boat, mind you) in Europe for a 2nd wife (my great-grandmother) when his first wife died.
Those stories tell me a little bit about the person that I didn't know before but nothing of this rich culture I'm supposed to embrace. I'm from America, and I'm American, 4th generation at the most recent, I'm not going to list 5 or 6 nationalities I'm no part of, except that's what people really want to know when they ask! It is more difficult to have this conversation with people more recently descended from immigrants or immigrants themselves. I really think the children of immigrants assimilate more than they realize - it gets watered down pretty quickly, but they are still so proud.