Part of citizens of the US referring to themselves as "American"...and most of the world doing so also...might be a bit of arrogance/nationalism/whathaveyou on our part. I think a bigger part is just practicality. What else do you call us in English? I generally introduce myself as Texan when I'm abroad (as most people know where Texas is).
The only country with that problem is United Arab Emirates. They are referred to as the Emirati (suggesting Americans could be referred to as Statesian), but the Emirati also refer to an ethnic group.
I can dig it.