North America isn't "the north part of America" -- the continent is named "North America."
So the nationality is American but citizens of the continent are North American or South American respectively.
The people's of North and South Americans aren't collectively known as "Americans." In French americain refers to "one who is from the United States." It's the same in multiple languages. Even Spanish refers to people from the US as americanos.
This is a subtle thing and in the grand scheme really makes no difference unless someone feels so strongly about it that they want to change multiple languages.
The American Embassy is not referred to anywhere (in English) as The United States Embassy --
edit: actually "US Embassy" is common, sorry for the misstatement. However American Embassy is very commonly used by diplomatic personnel and in general conversation. --
I don't understand why a certain subset of people, generally from South and Central America have such an obsession with this. Canadians never refer to themselves as Americans. In fact, many would resent such a thing.
Never, not once in writing or in speaking heard it referenced this way. American by itself references the USA, North or South America references the regions.
we're talking entirely different tectonic plates - plates that don't even touch. plates that will eventually shift such that you there will be no possible land travel, and a widening gulf (admittedly in the distant future). not to mention different cultures, hemispheres, etc.
https://www.sta.be.ch/sta/de/index/wahlen-abstimmungen/wahle... (German)