-The "ian" or "ean" in 'Argentinian'/ 'Argentinean' contains and can be felt as a put-down or diminishment of what some thing or person actually is. Like describing something or a person firmly connected to or identified with Scotland as "Scottish" rather than "Scots", "Argentinian" suggests that a thing or person is just 'sort of like' in some way(s) something that is wholly and exclusively of Argentina.
I was taught this by a Scots' friend who quite rightly objected when I called her 'Scottish'. Perhaps the Scots are more sensitive to this than Argentines are. But even if Argentines take being called the wrong thing with a grain of salt, the wrong word is stilll tinged by just saying that a thing is less than it is.