You're being a little pedantic. It's usually understood to refer to US citizens by just about everyone outside the USA as well, not just US citizens themselves.
As an "American" from the South, and having friends in both Central and North, we constantly make fun of the fact that we can't call ourselves Americans the way Europeans and Asians do.
Another "interesting point" though is that the Indigenous population are still called Indians and the the real Indians are not identified as Asians.
Not all taxonomies consider "America" as one continent. In geography school we were taught of North America and South America as different continents. And if you check Wikipedia, you'll see there are several ways to divide the continents, and they cound from 5 to 7 depending on how you look at it, IIRC.
>Another "interesting point" though is that the Indigenous population are still called Indians and the the real Indians are not identified as Asians.
In my corner of Europe we don't consider the "real Indians" as Asians either. Some cultures do, but we prefer to reserve the "Asian" moniker for the far east (Malaysia, China, Indonesia, Japan, Korea etc). I don't see much cultural or historical resemblance between these and Indians.
Actually, there is: "US American" [1], though it's rarely used.
Also, FWIW, my understanding is that the word "european" when used by americans and britons carries a mildly prerogative air of "frenchness". It certainly isn't a purely neutral geographical term.
We use "The Americas" to refer to the continents as a pair, and prepend a cardinal direction to refer to one of them individually.
Citizens of the Commonwealth of Australia call themselves Australians, despite there being other governments on the continent of Australia.
Speaking as a Brit, we do (rather ignorantly) generally refer to citizens of the U.S. as "American."
It's a cultural/linguistic norm, not a programming problem. Don't try to reason it out as rigorous logic.
https://www.youtube.com/watch?v=NVMZC4y4zXU
tl;dw? Skip to 3:40.