Let's see what you guys think of this logic.
a) The dominant culture in the United States is European. (More specifically, largely British.) The language, religion, legal system, ideolog(ies), cooking and sewing and building and working and farming traditions, are all of European origin. So why should the Europeans dislike the United States? After all, Americans are pretty much Europeans, and so disliking America is disliking yourself, if you're European. The dislike must, therefore, be due to some outside, non-European influence.
b) American Indians had a great deal of direct influence on the way early Euro-Americans lived. Euro-Americans adopted some farming methods and the like from the Indians. Unfortunately, there were too few Indians (when the Pilgrims landed the East Coast Indians had already been literally decimated by smallpox; 90% had died of a smallpox epidemic most likely caught from fishermen, who'd been up and down the Atlantic coast ever since at least 1500 AD) to have much of an effect on the European-Americans beyond basic practical stuff about planting corn and the like. And, anyway, the European-Americans killed some 20,000-40,000 of them in the frontier wars. So we can't really say they've had too much of an effect on making modern American culture what it is now. They haven't made Americans really different from Europeans.
c) Asians have never really come to America in large numbers until after World War II. While they've certainly played an important role in US history, from the Chinese labor gangs on the Central Pacific railway to the shameful deportation of the Japanese in California during World War II, again, there just haven't been enough of 'em until very recently to have made a defining difference between Europe and America. Not that Asians don't add a valuable flavor to American culture and all, they add to its dynamism and to its sheer variety, but they play the same role as they do in most European countries, which have Asians too. So that's not a major difference.
d) Hispanics have certainly played an important role in American history, and I would even argue that the Hispanic influence is important enough to be defining. Part of what makes America what it is--the cowboy tradition, the clothes we wear around the world now, Southwestern architecture, Texi-Cali-Mexi food, horses and cattle and ranching, border bilingualism, country and western music, large-scale grain farming--is due to Mexican Hispanic influence. And Puerto Rican and Cuban Hispanics give a distinct Caribbean flavor to many Eastern cities as well. (They've added to my diet, anyway, and for the better.) But that's all stuff that the Europeans like. At least they say they like it in its original, Latin American form. They love Hispanics when they're in Latin America. It's very hip and all. So the Hispanic influence in United States culture is not what irritates the Europeans about the US.
So it must be down to e) the African Americans. Now, the first blacks were landed in Virginia in 1619, meaning that their forebears were in America since before 99% of white people's forebears were. At the time of the Revolution the South was one-third black, and by 1860 blacks were a majority in several Southern states. Black people have had a great deal of presence in and influence on modern American culture, especially popular culture, and especially in the South. And their presence will only become greater, since you have to figure that before America began to dismantle Jim Crow in 1954 (Truman had already integrated the Army) black culture was officially discriminated against, and yet it still bubbled up like lava, unstoppably. Give it fifty more years of relative lack of racism and watch it flourish. Popular music and dance, folktales and legends, food, religion, dialect, and almost four hundred years of common history in the New World show the continuing major African influence on American culture. It is the basic mixture that truly makes the roots of American culture different from European. After all, Jim, the hero of the Great American Novel, The Adventures of Huckleberry Finn, is black.
Is this what the Old Europeans are objecting to?