This is such a common argument among libertarians and the MSM. It goes something like, "Of course Islamists hate America, we're always invading and bombing their country!" Sounds valid, but how much water does this theory hold?
I was reading an essay by Bruce Bawer called "Crisis in Europe", published by Hudson Review 2006 (link to article on JSTOR below), which puts forward an interesting answer to this question. In it he draws on the scholar Bernard Lewis, author of The Crisis of Islam:
"It's not American imperialism or exploitation that provokes Islamists but rather the seductive appeal of American culture, their own attraction to [it] which appalls them.... while outright Russian imperialism--including the Soviet Union's harsh suppression of Islam within its borders--has been a far more detrimental factor in the lives of Muslims than anything America has ever done. Russia has been criticized by Muslim leaders far less than America has."
Bawer's essay focuses on the topic of Muslim non-integration into European culture. For this reason alone, it's well worth a read. Here's more from Bawer: