Your America-first approach to naming is fine in American circles but don't be surprised when other people use other terminology. No, America is indeed a continent. I have a lot of Brazilian/Peruvian/Canadians colleagues and have been in contexts where we've discussed American (continent) vs European points of views.

I am not sorry if my attempt to use precise language when precision is needed is "disingenuous" to you. What a weird thing to get rude about.