Canada might be in North America but it does not make everyone on that hemisphere American.
doesn't America span both hemispheres?
I don't think anyone would say the Irish are American by virtue of being in the same hemisphere.
I assumed he meant the Western hemisphere, in which case, no, it doesn't span both hemispheres.
Regardless of how you define continents, 'American' or a word obviously deriving from it is how many languages refer to people from the USA specifically, rather than people from anywhere on the continent or continents of America. In my Danish course, I was told to answer the question of where I'm from with "Jeg er amerikaner
and my classmate from Ecuador was not. There is a separate word for that. There is not another word for people from the USA.
There is no country in Europe where its inhabitants are known only
as 'Europeans', so that's not a good comparison.