Particularly because I'm not sure I've ever come across a case in my life when a speaker or writer wanted to include people from both continents as a single group. It's just not a label that's useful for much of anything.
"North or South American" isn't a particularly meaningful or relevant concept at all. In contrast with e.g. "Latin American" which is very useful/meaningful.
And if people from the United Mexican States are Mexican for short, it's an easy shorthand to similarly call people from the United States of America, well, American.
> Particularly because I'm not sure I've ever come across a case in my life when a speaker or writer wanted to include people from both continents as a single group.
That's the thing: for many people, it's a single continent, called just "America", which can be further subdivided into "North America", "Central America", and "South America" (but these three are not continents, they're subdivisions within a single continent; another common subdivision is "Latin America", which corresponds to the countries colonized by Spain or Portugal).
That's fine, but it still doesn't change the fact that there isn't really a need for a word to refer to its inhabitants collectively.
The same way Oceania is often considered a continent, but nobody ever refers to people there as "Oceanians" in a way that includes both modern Australians and Polynesians, for example.
I'm just saying that calling people in the USA "Americans" isn't taking away from an otherwise useful/important modern-day usage. Regardless of whether you consider it to be two continents or one.
> Do these people also believe in a single continent called “Eurasia”?
It's the traditional six-continent model (America, Africa, Europe, Asia, Australia, Antarctica), which according to https://pt.wikipedia.org/wiki/Continente is the model taught in school in many places, including Italy, Spain, Portugal, and all over Latin America. So no, "these people" (which includes nearly all of America outside the USA and Canada) have learned about Europe and Asia as two separate continents.
On the other hand, the seven‐continent model is dominant in the Anglosphere. So it seems the sensible thing to do is what in fact is already normally done: in Spanish and other such languages, use “América” to refer to North and South America, and in English, use “America” to refer to the USA and “the Americas” to refer to North and South America.
Particularly because I'm not sure I've ever come across a case in my life when a speaker or writer wanted to include people from both continents as a single group. It's just not a label that's useful for much of anything.
"North or South American" isn't a particularly meaningful or relevant concept at all. In contrast with e.g. "Latin American" which is very useful/meaningful.
And if people from the United Mexican States are Mexican for short, it's an easy shorthand to similarly call people from the United States of America, well, American.