I like you do not feel that he is the president, for the simple fact, he is not a natural BORN NOT NATIVE of the US. You are looking at by birth. I AM the constitutional question of what defines that natural born status.
This may seem a strange question, but I believe it is the real "test" to nationality.
If I'm an American, why would I be supporting Mexico in soccer, or If I were a Brit, why would I be supporting Pakistan in Cricket?
Of course nationality and "Citizenship" have morphed into one, which has helped dilute the issue.
Which makes us all citizens of the world :-)