been many times to various LatAm countries and the opinion they have on what constitutes "America" is vastly different to what we in the Anglo world think of it.
There's songs, poems , books and general culture that refer to America as a unity of the entire continent and most of them refer to "Americanos" as the people living in the entire continent not only the USA
we were taught in "America" (the US) that America is only the USA and the rest is basically not there/not important and/or NOT America but North and South America -and sometimes Central America doesn't even exist- ..the excuse being that it's short for Unites States of America. (I use it like that btw I say America as in the USA )
Hell, some of the people I know -in the States- even think of Mexico as South America and will die swearing it's like that and they'd say it's not even part of America
so for Argentinians they call themselves Argentinos yeah but they call themselves Americanos also-as in being part of the Americas- same could be said for other nationalities -they literally have told me so