I think people self identify, to a great extend, based on their physical appearance.
What was Obama's biography named?
Was is
a. Dreams of my Father and MOther?
or
b. Dreams of my Father?
Don't look it up, just choose.
So?
It’s not like he disowned the white side of his family.
If anything, he was more influenced by them.
What do you base that conclusion on?
He spent more time with his mom and his grandparents on her side. His dad left.
And despite that, his dad got top billing.
Physical attributes, or as you put in "melanin", trumped those that actually raised him and loved him.
What are you talking about? Top billing?
He wrote a book about how his father left him.
https://www.amazon.com/dp/B000N2HCM4/?tag=usmb-20
"In this lyrical, unsentimental, and compelling memoir, the son of a black African father and a white American mother searches for a workable meaning to his life as a black American. It begins in New York, where Barack Obama learns that his father—a figure he knows more as a myth than as a man—has been killed in a car accident. This sudden death inspires an emotional odyssey—first to a small town in Kansas, from which he retraces the migration of his mother’s family to Hawaii, and then to Kenya, where he meets the African side of his family, confronts the bitter truth of his father’s life, and at last reconciles his divided inheritance. "
Sure, his father left him, his mother's parents raised him, and his Father gets top billing.
Here is Obama talking about race, and his perception of himself and his heritage and his daughter heritage.
Barack Obama on Race, Identity, and the Way Forward - The Atlantic
"Coates: I wonder how you came to think of yourself as black and why.
Obama: Well, part of my understanding of race is that it’s more of a social construct than a biological reality. And in that sense, if you are perceived as African American, then you’re African American. Now, you can—that can mean a whole lot of things. And one of the things I cured myself of fairly early on, and I think the African American community has moved away from, is this notion that there’s one way to be black. And so you are right that I could have been an African American who worked for an international organization and was not engaged in the day-to-day struggles, politically or culturally, that the African American community faces. There are a lot of African Americans who may make those decisions, and they’re still African American, but they’re just living their lives in a different way.
I think for me, first and foremost, I always felt as if being black was cool. "
Note that he does not correct the interviewer. He does not state that he sees himself as multiracial or both black and white. He is black.
And here, he talks about his daughters'.
"Obama: I think it is. It’s interesting watching Malia and Sasha, who have obviously lived in as strange and unreal an environment as any kids do. They feel very strongly about their African American roots. They don’t feel that they have to choose. And that, I think, is a great gift to bequeath them, where they know they’ve got a home, they know they’ve got a base, they know who they are. But they don’t think that in any way constrains them. And certainly they are not burdened by the sorts of doubts that previous generations—and even our generation—might have felt in what it means to be black. They think being black and being free are not contradictory. It’s interesting, when we went to visit the museum, Smithsonian [National Museum of African American History and Culture], just watching them soak it in. And they’re well-informed young people, so they knew most of the history, and I forget which one of them just said, “I can’t wait to bring my friends here.” And I think she was not just referring to African American friends but her white friends. She said, “Because face it, our stuff’s cool.” We’ve got Michael Jordan, Beyoncé, Dr. King. What you got?"
They feel strongly about their African American roots and have such contempt for the heritage of their grandmother than they don't even discuss it,
and go on to plan to gloat to their white friends how great her culture is and how lame their white culture is.
IF, your view of the world was correct, Obama should have corrected her and reminded her how much he and she owes to her white grandmother and great grandparents, and how rich and "cool" their culture is too.