I'm staying out of this intercontinental battle, but I'll just point out it's interesting that the offensive national stereotypes are asymmetrical in that the ones about people from the USA seem to be the same everywhere, whereas the ones in the USA seem to only be perpetuated there (also Canada, presumably due to the overwhelming cultural influence from the USA).
US Americans are fat, ignorant, arrogant, jingoistic etc. This seems to be the stereotype everywhere.
Brits have bad teeth, French are pretentious cowards, Irish are alcoholics always fist fighting - In the USA - only found elsewhere where US cultural influence has imposed them.
I know there are stereotypes like Italians gesticulating a lot which are both in the USA and outside, I'm just talking about these ones in play.
Going back to the formative years of the USA, you can see why people might feel insecure about the main two powers operating there, the British and French, and want to defensively mock them. When it comes to teeth, it's actually people in the US who seem to be worried about their teeth with all the cosmetic procedures they have done on them. That's the best I can do at explaining these tropes' origins. ¯\_(ツ)_/¯