Some of the problems with the teacher's questioning is that:
A. If Wu was born and raised in the U.S, he would really just be like any "American" in the class in terms of historical knowledge/insight so far.
B. Singling him out because of his race/ethnicity
C. Not the "Asian" that was being lectured about.
You're right, and I can confirm that, having grown up in one of the most diverse areas of the U.S., environment certainly seems to play a bigger role in personality/culture than does race.
So, asking an Asian American for some "Asian" perspective is as you say, futile. However, for people not born in America with whom race corresponds to a foreign nationality, race can be a much better indicator of cultural difference, not because race causes the cultural difference (although I'm sure it causes SOME, even for American citizens in the same environment), but because it is strongly correlated with being of a different nationality, the nationality difference being what brings the different culture. So in the case of foreign nationals, you CAN ask about race with a reasonable expectation that the underlying culture will be different.
Regardless, race is interesting to me even of people of the same nationality, where the cultural differences aren't so obvious. Yes, you are correct that there is a beautiful similarity between ALL humans, but there is also a beautiful and interesting (and quite pronounced) physical difference between all the different races of humans. Isn't it interesting that people look so different? Asians, Arabs (this is not a derogatory term), Caucasians, Africans, South Americans, Indians... it's just interesting to notice, like trying a wide variety of food or something.
Why does the physical difference between races matter, if your personality is "inside", you ask? Well, I'm not so sure that the personality is actually inside. This cannot be proven empirically, but personality might show on the face, so to speak. Even though the dominant paradigm is that the physical appearance of somebody doesn't in anyway correspond to their personality, this may not be true, and we certainly don't go through life as though it is. We are always making judgments about people based on their looks, even amongst physical variations among a single race. By extension, we also do this for different races.