They have differing beliefs and the easiest way to unify people is to provide an external enemy.
So you were wrong.
The Muslim hatred of the west has nothing to do with "cognitive dissonance" of the west.
It is simply that Muslims are wholly intolerant of anyone who does not agree 100% with their own peculiar beliefs. They hate everyone who isn't them, including Muslims who aren't exactly like them. We are not them. Therefore they hate us.