It's a cultural difference. As a foreigner, the American way of exaggerating everything has always amazed me. They don't even notice themselves, so expect more of these "what's odd about it?" reactions.
I think what sets Trump apart is how straightforward his hyperbole is. It's present throughout American culture but it's usually a bit more subtle. It's even in basic things like answering "How are you?" (in the US, "great!" is a neutral answer and "could be better" would be cause for concern - in e.g. Germany on the other hand, "great!" would prompt a request for elaboration whereas "could be better" would be understood as fairly neutral).
I also haven't seen another country (in Europe at least) where politicians across party lines so frequently emphasize in so many ways how great their country is - not even in a jingoistic way, just as a shared cultural consensus.
