It's insulting because it implies that people of mixed race are more "messed up" than those who are not as obviously or identifiably mixed race. What you described happens to lots of people - not just mixed race people are called "not Black enough" or not accepted by whites. And truthfully, most Black people in the Americas are mixed and can look any kind of way - there's no magic look for "biracial" or mixed people. I think the "torture" you described happens for all, or most, Black people what with shadism, racism, post-colonialism, etc. Those of us who are mixed don't have any special claim on that.
Also, Obama has the right to define himself and I find it insulting when people TELL him or anyone else that he is "both Black and white' or "biracial" or whatever. Yes, he has African and European ancestry, but HE has the right to say whether or not he considers himself Black, white, both, neither.... some people seem to have this utopian but strangely rigid view that if someone has a Black parent and a white parent, they MUST be this "biracial" poster child who is both races, gets crap from both races, has the ability to be, or should be, "accepted" by both races, has the best of both races, identifies equally as both races.... and it gets tiring to me because there are a variety of possibilities for that person's identity, and identity can be fluid and/or take on multiple identities, so why try to pin someone in a "biracial" box?
Get used to me. Black, confident, cocky; my name, not yours; my religion, not yours; my goals, my own; get used to me. -Muhammad Ali