He called himself African American for a purpose he spoke about he couldn’t disown his white grandmother (over fears that she had) when the issue came to light about Reverend Wright.
That was refered to throwing his grandmother under the bus.
There is no need to study the issue. He had a choice during the elections in Illinois and during the presidency.
Again, realistically, there is no man in the United States with the complexion of Barack Obama, regardless of his heritage, that would be accepted as “white.” He had no more “chance” than Al Sharpton of claiming he was white. And what you call “throwing under the bus” I call recognizing weaknesses within one’s own family.