Theories of terrorism
Reprisal theory: They kill us because we killed them. Proof: look, we killed them. Doesn't take a genius to figure this out.
Aggression theory: They would kill us whether or not we killed them. Proof: look at all their targets - not just big bad US. Notice all the hot spots (Sudan, Indonesia, etc.). Threats against non-Muslim artists and writers. See Religion theory. See Shark theory. See Theater theory.
Synthesis theory: They would kill us whether or not we killed them, but they kill us more because we killed them. Proof: see Reprisal theory and Aggression theory.
Shark theory: They smell blood in the water. It is our weakness that attracts them. Proof: Their rhetoric, our obvious lack of resolve. It would not be the first time someone was attacked because he was weak.
Religion theory: Their interpretation of jihad instructs them to attack us because we are nonbelievers. Proof: Their rhetoric. Their many religious explanations of what they are doing and why. Their violent attacks on apostates, disrespectful nonbelievers, Christian schoolgirls, Buddhists, Muslims of the wrong sect, Jews, etc.
Theater theory: They attack us primarily to impress other Muslims and gain power, adherents, and influence within and outside the Middle East. Proof: “When people see a strong horse and a weak horse, by nature they will like the strong horse” (Osama bin Laden). This is often the effect (see attack on Israel from Lebanon); it is not unreasonable to suppose it was part of the motivation.
[updates] Clausewitz theory: Governments encourage, protect, and fund terrorism to achieve cold political purposes. Politics by other means. To attack and distract and weaken enemies with deniability, to deflect attention of restive subjects.
Die Hard theory: It's really for money. Terrorists receive ransom in various forms. So do governments.