Earlier quoted context omitted.
What would it mean for Portugal if Spain decided to change its name to Iberia? This is exactly what is happening here. They want to be named after a geographical region which is way bigger than their borders.
Yea, it's as silly as a country claiming to be the "United States of America" when lol, Canada and Mexico and all of South America would like a word...
In Central/South America, it's generally taught that everything from Nunavut to Cape Horn is a single continent, America. When the US calls itself "America," that's seen as a deliberate attempt to claim primacy over the whole continent.
In English-speaking North America, it's generally taught that "America" is the country and "North America/South America" are the continents, so we're befuddled by the irritation.
This is why Canada, actually, doesn't appear to have an issue with the "America" thing.