What you're saying is he has certain qualities that atheists (and other people who aren't atheists) have but that aren't essential to being an atheist, and certain qualities that Muslims (as well as other people who aren't Muslim) have but that aren't an essential part of being a Muslim, and that this makes him both an atheist and a Muslim, and you're wondering why people don't understand?
I'd say that he's a functional agnostic. It would be hard to reconcile a 100% belief in Islam with the other parts of his life. Not unless there's some secret room at the White House where he prays 5 times a day.
Yet Islam has some moral prohibitions that Obama doesn't want to follow. Every religion other than atheism has limitations or exclusions on smoking, drinking, fornication, and abortion. Obama does not want to heed those prohibitions or limitations, hence his embracement of secular humanism/ atheism/ agnosticism (which are fundamentally the same in morals, hence it's easiest to call them all atheists).
There are many, many examples which show that atheism is morally bankrupt, and that any morals they exhibit are strictly for pragmatic purposes. Here's one.
He fuses the worst parts of each ideology. "Atheist Muslim" (or the inverse) is the easiest description of his ideology.