When you say that your ethnicity is American, there is no American ethnicity. You had to throw away your ethnicity to become American, that is what it means.
The American ethnicity is a transplanted "Western Civilization" ethnicity. This is the culture. It's Greek culture, as evolved into Roman culture, as tempered by Medieval Germanic. Our legal system descends from the British Common Law. This is who we are.
Anybody who says "You can't talk about European American White culture, you have to take a specific European ethnicity, you have to be Irish or Italian or whatever", can be replied to with "Well, you cannot then have a Black culture, you have to identify with a specific tribe, then".
But don't bother saying that in front of the professor.
THE CLASS IS A TRAP, used to discover and expose non-liberals, so they can be excluded from whatever lib-dominated profession the class is a prerequisite for. Just say what is expected, pass the course, and move on.