"My father came from a Kenyan family that includes many generations of Muslims."
In both of Barack Obama's autobiographies he states precisely that both of his fathers were Muslim, and that he, himself, was considered born into the Muslim faith because of his fathers' religion. He also wrote about his mentor, Reverend Jeremiah Wright, who was an open practicing Muslim at one point. In addition, a disproportionate percentage of Obama's close friends are or were practicing Muslims.
After being elected President of the United States, Barack Obama went overseas and explained to the Muslim world that he was a Muslim and he did it by describing his Kenyan father and the generations before his father as all Muslims. That is why Muslims believe that he is of their faith and why many Americans do also. Listen to his own words.