There are two parts to these attitudes, and the largest problem is that people in the USA often conflate them. One part is satisfaction (and yes, pride) in real invention, innovation and achievement. I have no issue with this part. People in the USA have done much to warrant some pride. This shouldn't take anything away from people in other nations who have their own achievements.
The second part is the idea of American exceptionalism: that the USA is great because it's the USA. This is nauseating, indeed. It's also obviously harmful, since now "greatness" is a birthright rather than an achievement.