Those who can, do
The U.S. was the "global hegemon" for much of the post-WWII period. Europe was unable and unwilling to take a leadership role after cannibalizing itself in two consecutive world wars, so the U.S. did, and in the process established a peaceful international order and international financial stability. Unfortunately, maintaining international order doesn't work by sitting on the sidelines and letting others do as they will. To take another British example here, look no further than Neville Chamberlain's behavior at Munich. That worked out really well, didn't it?
International isolationism is not possible for effective world leaders. The U.S. is still the most powerful leader in the world, and has to become involved in other states' affairs to
prevent the kind of international conflict that Europe previously perpetuated for centuries. Others want us to. South Korea wants us involved, Europe wants us involved, Japan wants us involved as, I would suspect, does China and Russia. Because the U.S. helps to ensure peace. It is overly simplistic and more than a bit naive to say that the U.S. just picks on weak states for political gains, and backs away from any real challengers. European anti-Americanism is no more sophisticated or fact-based than the jingoistic pro-American rah rah stuff you are referring to.