This Rasmussen Reports article shows that relatively large numbers of Americans believe the U.S. has been arrogant towards Europe, as in fact the President admitted on his recent trip to the region. I believe this is debatable but for sake of discussion, let's assume it is true.
The more relevant issue is whether the attitudes and general wimpiness of Europe have justified arrogance on the part of the U.S. toward Europe. They have kindly allowed the U.S. to pay for most of their defense since the end of WW II. While we spent billions on the military, they spent their tax dollars on various socialist programs which they suggest to us we should emulate. As if....
Charles de Gaulle's famous quote about France applies to Europe generally, "How can you govern a country with two hundred and forty-six varieties of cheese?" Europe is fun to visit, a sort of adult Disneyland, but it isn't always easy to take Europe seriously. If there has been arrogance, perhaps it has been justified.