There is a difference between arrogant egotism and justifiable pride and authority. The United States of America is more powerful than any nation has ever been. The US could compete with the rest of the world combined. As such, we are often the subject of scrutiny, and if ANY country was scrutinized as carefully as America, terrible problems would be found.
For all self-righteous Europeans who think America is such a misguided, evil country: I would like to point to France's Jean-Marie le Pen, an ultra-nationalist, xenophobic, antisemitic, authoritarian rightwing nutjob. This Hitleresque figure (indeed, he associated with Nazis and several ex-Nazis are in his party) is not an isolated psycho or a single embarassing man, he has captured 15%-20% of the popular vote in France. Imagine how horrified the world would be if a man who wanted all non-whites evicted forcibly from the US and advocated the rounding up and forced imprisonment of those with STDs like AIDS won that much of the American popular vote. Its because we're simply more influential that you would hear a greater outcry. Jean Marie le Pen is a terrifying figure and an embarassment to France, but because France is not as important, he gets no international attention. How many people have ever even heard the name before?
America is no more troubled or egocentric than any other country, our blemishes are simply more noticeable.