You might remember the question of "why do they hate us?" from American life immediately after the 9/11 attacks. People asked it because they wanted to know what, if anything, they had done to motivate the hijackers to commit such monstrous crimes. This question figured prominently in Art Spiegelman's "In the Shadow of No Towers" so I thought I would put down some of my thoughts on the topic.
Although the question of "why do Islamic terrorists hate us and want to kill us?" mostly applies to America and our terrorist opponents, it also applies to Israel as well. At first glance the question implies that Americans and Israelis must have done something wrong in order to have become the recipients of this murderous hatred. I don't think this is a particularly bad way of approaching the topic: In a dispute we can't control what the other side thinks and does, we can only control what we think and do. Demanding that the other side be reasonable might be necessary and might be right, but it could also simply lead to both sides yelling at each other to be reasonable.
What I have found when people attempt to answer the question of "why do they hate us" their responses come not from their own understanding of Islamic terrorists but from their own politics. People on the right simply claim that "they hate us for our freedoms" in other words they hate us for being different from them. Therefore the only solution to that kind of hatred is a bullet to the chest or a Predator drone to the head. People on the left, on the other hand, say that Islamic terrorists only hate us because we interfered with their countries and basically pursued our own interests there regardless of the consequences to the ordinary people.
I do think that both sides could make a compelling case. Although it is true that ordinary Afghanis, Pakistanis, and so forth could be and will be motivated to anger by US actions, it is also true that the leadership of Al Qaeda are principally concerned with what America is, not what America does. Although they claim it was American actions against Muslims that stirred them to anger, they are notably silent on the subject of Muslim vs Muslim violence. So it seems logical to conclude that they have a special grievance against "the Zionist-Crusader alliance," for having a different religion from them.
So I guess what I am getting at is that when people attempt to answer the question of "why do they hate us" they need to be willing to look at the facts first and put their politics aside. Although it may fit leftist ideology to believe that Hamas only hates Israel for Israel's actions against the Palestinians, a quick look at the Hamas Charter proves otherwise. To ignore new information is not only unscientific but foolish. That being said, this doesn't mean Israel and the US should not try peaceful means as well. Removing a terrorist group's foundation of support is almost as effective as destroy the terrorist group itself. They just need to be sure that the foundation is actually disappearing.