Why do some White people pretend to be Black? Or Latin, or Native American?
I think, for some white people who are stuck thinking in the ways that racism has taught us--stuck even more than they think they are--it seems like taking on the identity of a person of color will add to their interestingness and power, and give them entry to a fellowship of people of color that they think they couldn't enter otherwise. Of course, there's so much actual ability to enter into fellowship with anyone just by being an actual friend or colleague, listening, owning your own history and noticing your assumptions! And, adopting a false identity as a person of color does not require actually going through the experiences that really being a person of color would; so the white person does not actually have to give up the power or privilege they have received.
There is also a piece of legitimate uncertainty in the race some people identify as. As many people have pointed out, membership in a Native American tribe is not necessarily dependent on ethnic ancestry. And some people, like Shaun King, legitimately do not know who their parents were; and if you think about it, few people in the world could truly be said to know who their father is. I have sympathy for people like Elizabeth Warren, who were told as children that their family included and ethnicity that turns out to be at least partially false. In my own family, there is some evidence that a recent ancestor was Cherokee, but not all people in the family tree agree that that's likely.
As I've unlearned racism--an ongoing process--I've realized the ways that even in my support for people of color, I have sometimes engaged in a version of racist thinking. To pretend to be black -- whether overly, or in the partial impression you might give -- is to essentialize race, as though you couldn't communicate the things you bring and the things you need without using race as a manipulative tool.