As noted, this subject has come up before. You can find examples both in GD and the Pit.
However, it begins with a false premise, and so “factual” answers are going to be unattainable.
First: “Europeans” do not dislike Americans.
There are specific small groups of Europeans who dislike American foreign policy or American tourists or American TV shows and movies flooding their theaters and TVs or American capital punishment or a number of other aspects of things American.
However, even within these groups, you will find people who despise our foreign policy who still think that individual persons from the States are quite nice. The blanket statement that “they” dislike “us” is simply wrong.
Second: A certain amount of feelings directed toward the U.S. are inspired by the sheer size of our presence in the world. We (or some percentage of unperceptive U.S. citizens) used to spend a lot of time “hating” the Russians because that nation was a very visible threat to our nation, while we rarely spent much time having any thoughts at all about people from Togo (if we could even find enough Yanks who knew where it was).
The U.S., however, is so large and powerful, that it is impossible to ignore it. Whether it is exported culture, extended military presence, or economic club wielding, nearly everyone in the world encounters some aspect of the U.S. every week, so they are all going to have some opinions. And if everyone has an opinion, some percentage of those opinions are going to be negative.
Third: Europeans (and Asians, Africans, South Americans, Oceanics, and North Americans) all have opinions of their own neighbors that can vary from the warm and friendly to the disdainful to the antagonistic. I have seen a few reports in recent years that American tourists have fallen below the Germans and the British as “most hated tourists” in several countries. The Germans and French and British are always taking cheap shots at the others–and lots of people pick on the Italians. So feelings toward Americans are simply expressions of the attitudes that all people display toward all people–and as Yanks, we tend to notice more thje comments directed at us.
Finally: there are silly statements such as those posted by Susanann that reinforce stereotypes that the U.S. believes that the rest of the world should hold us in some sort of awe and that the only bar to that admiration is jealousy or resentment. While that attitude is not held by all Americans, enough people express those attitudes that some Europeans tend to think of Americans as needlessly arrogant.
And, as hajario notes, there are many people who actively like Americans. My first trip through Europe was during the Vietnam war when there were many anti-American protests going on. In eleven months, I encountered only two people who were rude to me as a foreigner, and I cannot say that it was my nationality (as opposed to by foreignness) that triggered either insult. Even in France, where lots of Yanks claim that they “all” hate us, I was treated hospitably on many occasions and never met actual anti-American prejudices.
