If you called a proud Canadian "American", he'd likely be offended. The same goes for many people from other countries in North, Central, and South America.

As for the term "American" being derogatory, I suppose it is to some but certainly not to many people from the US. Even the US Military Code of Conduct begins,

I am an American, fighting in the forces which guard my country and our way of life. I am prepared to give my life in their defense.

No, I suspect that most of us aren't in any way ashamed to be Americans no matter how much some others seem to believe we should be.