I was at this seminar last summer and when everyone was introducing themselves, I realized that we usually don't tell people our ethnicity when we meet them. What do we tell people when we introduce ourselves? In most situations, we tell people our:
4. Where we're from
Sometimes we tell people about our family (i.e. "I have a wife and 2 kids" etc) or about our education (i.e. "I have a Ph.D in..." etc). But we almost never tell people about our ethnicity (i.e. "On my mom's side, I'm half..." etc). Unless we're meeting people in a culture-related setting, the topic of race is almost always avoided. Don't get me wrong, I guess that's a good thing.
This seminar I went to was pretty ethnically diverse. We were introducing ourselves one by one in front of the audience and I was imagining what would happen if someone mentioned their ethnicity in their introduction. If someone did, the worst that could happen would probably be a quiet awkwardness in the crowd. It would definetely be awkward, but why? For some reason, it's more awkward than saying your age, job, or hometown.