Well, everybody born in the american continent is technically “american” too, including Central and South America. Is there a specific term in english for these people?
Edit: Thanks for all your answers, especially the wholesome ones and those patient enough to explain it thoroughly. Since we (South Americans) and you (North Americans) use different models/conventions of continent boundaries, it makes sense for you to go by “Americans”, while it doesn’t for us.
Stick with "American" because not only is it partially accurate geographically, it's completely accurate in terms of how self-centered we are as a nation as to think we're the only ones who count.
US bashing is getting old, tired and trite.