I think a reason this is less noticeable to people from the United States is because our continental model is different from the model taught in Latin America (7-Continent vs 6-Continent). In Argentina, for instance, you're more likely to learn there is one continent called 'America' that encompasses what people from the US consider two continents - North and South America. So for a person from the United States there is no conflict in referring to people from a continent vs. their own country because they are all distinct. A person could be 'North American', 'South American', 'American' or even 'Latin American' and the terms are completely clear and distinct to someone from the United States. There is no term that groups people from both North & South America together in English (that I am aware of). This naturally causes problems for people that don't think about continents that way and feel that 'American' referring solely to people from the US is condescending because it uses the continental term they are accustomed to and also excludes them from it. While I agree it is condescending, I think it is unintentionally so, and it is rooted more in language and geographic convention. While I try to be aware of it and avoid using the term 'American' where it might cause offense there isn't a widely adopted alternative in English. The opposite is the case in Spanish, where it would be quite rude to refer to oneself as American when one means Estadounidense because thats the term that matches the culture, language, and convention.

But American is just shorthand of United States of America, and rolls off the tongue better.

I postulate that most Americans aren’t trying to claim all of the Western Hemisphere, it’s just what’s currently being used.