Samuel Huntington warned about the "arrogance" and "unilateralism" of U.S. policies when Bush was still governor of Texas.
Europeans do not fear that the United States will seek to control them; they fear that they have lost control over the United States, and, by extension, over the direction of world affairs.
The EU, most of its members believe, enjoys a natural legitimacy, simply by virtue of being a collective body.
[The UN Security Council] has never been accepted as the sole source of international legitimacy, not even by Europeans. Europe's recent demand that the United States seek UN authorization for the Iraq war... was a novel — even revolutionary — proposition.
The core thesis, though, does not really stand up. Under the title "The Importance of Being Legitimate", Kagan says:
Europe matters because it and the United States form the heart of the liberal, democratic world. The United States' liberal, democratic sensibilities make it difficult, if not impossible, for Americans to ignore the fears, concerns, interests, and demands of their fellows in liberal democracies
That ignores the role of dissent within the USA and within Europe. The fact of the invasion of Iraq was that it was always controversial, opposed from the start by a substantial minority in America and a majority in Europe. The (spurious) issue of "legitimacy" was used tactically by opponents in Europe. They did not decide publicly that the legitimacy of military action would from now on always depend on specific Security Council authorisation; a clique in the media just chose to pretend it had always been that way, and a majority of the population believed them.
Similarly, the anti-war faction in the US did not oppose the war because it was "unilateral"; they cried out for "multilateralism" because they were against the war. If the invasion had been overwhelmingly popular with the US population, on its merits, nobody would have cared whether Jaques Chirac agreed or not, just as, when action in Yugoslavia was generally desired by Europeans, no-one saw any need to bother the Security Council for permission.