This is an interesting perspective. I agree with everyone's right to identify as they see fit. I am of mixed race and that is how I see myself, although I'm often assumed to be white or Latina or even Asian, depending on who is looking at me. Nope, I'm just black and white with a bit of Indian thrown into the mix. I embrace both sides of my heritage.
But I disagree with you on something...your coworker most likely is going by what he sees. I'm not sure why you would be offended if somebody thinks you might be biracial or multiracial. It's not an insult. Obviously he can tell that you are mixed with something besides black. I am VERY proud of my black heritage, but I also know that my appearance is not what people typically think of when they think of a Black woman. I'm very fair-skinned with "white" features, but my hair is kinky...that is the only feature that makes people question my ethnicity. The questions/comments/stares are annoying, but it is part of being mixed.
Some people can tell I'm mixed, some can't. It is what it is. You have the right to be who you are and to identify as you see fit, but some people will wonder if you are mixed because of your phenotype. It kind of comes with the territory. As long as you are secure in your identity, it doesn't matter what others think.
And I'm not sure how some biracials have created a backlash against other mixed-race people because it comes down to the fact that identity is a very personal thing. No one can define it for you. They can try, but only you know who you are. When somebody asks what my race is (I hate that question), I tell them I'm mixed and keep it moving. Saying that you are mixed doesn't mean that you are denying your black heritage or negating that part of yourself.