But I think you’re missing that this isn’t just a labeling, being African American is also about ones experiences in America. Obama is indeed African American because he both had experiences that tend to be common among black Americans (including experiencing white supremacy) and because he embraces that label. I’m not sure it’s on us to police those lines, as white Americans. You could also question my own sense of an Irish American identity, but it’s not for you to say. Identity isn’t just about race, circumstances of birth, gender, sexuality, skin color, what have you, but about how one experiences the world, too.
And keep in mind that African American was a chosen identity by many African Americans, as a means of both staking a claim in their Americanness and highlighting how systemic racism has worked to exclude a people who have been here, generally speaking far longer than, say me or mine.