It is just a completely different cultural mindset, while in the US they teach them there are 6 continents, in latin america they teach us that there are only 5. I am Mexican and I grew up there, and we only learned Europa, Asia, Oceanía (the Australia continent), África and América. They always referred to the US as "Los Estados Unidos" and added "de Norteamérica" when utterly necessary. We were taught the north/central and south is only a subdivision. The continent was named America after Américo Bespucio (Sp?) after he drew the first map of the whole thing (from Alaska to Tierra de Fuego). We latin americans feel as though we were being discriminanted when we're denied to be called "americanos" even though we were born in América (that which we were taught when little - again, totally different mindset). Actually, there is people from the US that place Mexico in Central America -not north-, and it also feels discriminative.
This kind of thing also happens when a capital city is called the same as the country (México, Panamá, Guatemala). In Mexico there is a city AND a state called Mexico. People from the country are called Mexicanos, people from the state are called Mexiquenses, and people from the city are called capitalinos ("from the capital"), or Chilangos (bad name people from other cities usted to call us but now we adopted it) or defeños (derived from DF - Distrito Federal). But sometimes, when they ask you "Where are you from" and you answer "de México" (referring to the city) they get angry ( but then again, when they go to Mexico city -for shopping or Something - they say "Voy a México" and not "voy a la ciudad de México".
So, I think people from the states are kind of correctly called Americans (and North Americans and "estadounidenses"), but Argentines and Mexicans and Brazilians are also americans.