I don't really have problems giving Americans credit for a lot of innovation, but I cannot say I feel induced to do so when too many American use it as a pissing contest to claim superiority.

It is totally fine to be proud of things your countrymen has achieved, but once you start using those achievement to say: We are better than you, then you overstepped a boundary.

Innovations are built on top of each other from things and people all over the world in complex networks. We got our numerals from India and algebra from the Arabs. The Greeks invented the mathematical proof and so on.