I believe terrorists, or even non-terrorists in the countries that the US occupy for that matter, hatred of the US policies is even simpler than discussed already. Think abou it for a while and think about if you had a foreign military currently occupying the U.S., killing your citizens (collateral damage of course), dictating policy and telling US citizens that we are here to liberate you, would you be pissed and fight back or lay down and say to yourself "wow, they are really here to help turn or country into a democracy"?
Why does the US always have to be the policemen of the world? And if the US citizens really believe the US foreign policy line that it's about building democracies around the world, well I guess I don't know what to say. Follow the money trail and that will tell you all you need to know as to the reason for "nation building". Telling the world we are trying to build democracies is a convenient excuse for ramroding our foreign policy on other nations, where political reasons or natural resources are the prize, pure and simple.
I don't condone terrorism and the US military needs to kick *** when provoked and when there are legitimate reasons to go to war (e.g., WWII), but the US has been blinded by their own foreign policies for decades now by inciting revolutions around the world in different countries and then objectively wondering why "terrorists" hate us. **** I would begin to loathe foreign militaries that occupied my country and turned it upside too.