As I understand there are to thing going on here, ethnicity (the biology factor, genetic markers) and nationality (the social factor, the sense where one belongs). And when discussing thing like these one should be specific.
With today's globalization it becomes harder and harder to defined nationality which is the main reason of those two to start so many debates. Race/ethnicity are genetic markers that one is born with that will determined how you look like, and the is actually very little one can do for that or cast blame at. One can't help being born to a certain "race".
Take me for example: My ethnicity is mixed since I have ancestry from South America, South Europe and Scandinavian. My nationality have been also mixed since I was born in Sweden but live my first years in Argentina (which is where my parents where born), but the last 25 years I I have live in Sweden. I would define myself as Swedish but every time I'm say it, people look at me and say "yeah but where do you come from?", even though I have a classic Swedish name and and the only thing that's different in me from that traditional Swedish girl is that I'm not a tall, thin, blond and that I speak with a very slight accent that that comes from a mix of speaking Spanish with the family and Värmländska (a Swidish dialect) used with friends while growing up. The funny thing is that when I'm in Argentina and say that I'm Argentinian (both because ancestry and because I have a dual citizenship) they still say , "Yeah but where are you really from?"...
When people say thing like "I'm proud to be ..." (even though the person/s uses generic words such as black, Asian, white, Latino on so on) is because the person fells proud to belong to or feel affinity to a certain group of people.