As an immigrant, I think that America is the greatest country in the world, at least from 1940 to today, and Americans should be really proud of their country. That's why so many people from other countries want to immigrate here.
Yes, there are problems, and yes, some countries in Europe are equally good, but there is no other country that is better. And of course, even in those countries, there are good areas and bad, as in the States. Obviously, a small country like Denmark is more homogeneous than a huge country like USA. One difference is that it is much harder to relocate from (for example) Bulgaria to Denmark, than to relocate from New Jersey to Arizona. This is one of the great freedoms in the USA: if you try a little, and you are not afraid to search, you can find a place and a job you really like, and you are still inside the same country.
There is a lot of anti-Americanism in many parts of the world. Some of it is paid for by particular interests, for example Russia. Some other is ideological. And some other is simply out of jealousness. For example, in Greece there are (today!) a lot of communists who hate America because they really believe (or they pretend to believe) that life in communist countries (USSR, Cuba etc) is actually better than in the States. Even today, you cannot argue with them that Cuba is a failed state. All those people need to find something to reinforce their views, so they magnify every negative story from America. And focus on the negatives only. If you talk to them they will tell you that life in America is terrible and the health system is terrible and the health system in Cuba is wonderful. It is funny that some of them have immigrated to America but none of them have immigrated to Cuba!