Most of Europe, even France and Germany is not anti-American.
But they violently anti-single-superpover.
And here is the conflict comes. If the superpower keep telling them who they should do business with, then the balance wil tip against the superpower however big sentiments they have for the American way of life, the movies, songs Coca-Cola and so on....
This is more about dignity than politics.
Then there is a fear factor too...
Logically, what would stop the US doing whatever it wants regardless who is its ally, or friends?
So that's why the europeans prefer a multipolar world.
Not a suprise, the chair did not even cooled out after Condi Rice left Brussels, the EU signalled that they are ready to lift the arms embargo on China...
"During anti-war demonstrations in Britain left-wing marchers have unashamedly waved banners defending known terrorists ...."
... while the remaining 59.4 million other Brits quietly got on with living their lives.