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.
One way around it is just to say “I’m from the US”. I know it’s not quite what you asked but based on what everyone else has said about why we’re simply “Americans” then I suggest this as an alternative. Also like they said, referring to yourself by state of residence works too, for instance “Texan” or “Californian” since they’re basically just as well known as the US itself at this point.