History is full of examples of how two belligerent parties, by engaging in an escalating cycle of belligerence, keep playing into each others hands. Strategists on both sides hope to capitalize on the others' entrapment in belligerence and violence to provoke him to a violent response that will be self-defeating. A recent example is how Al Qaeda's attack on the US on 9/11/01 succeeded in provoking the US to attack Iraq, thus discrediting the US throughout the Muslim world, not to mention the rest of the world. The US did Al Qaeda's work for it. On the other hand, the Bush Administration seized on 9/11 as an opportunity to invade Iraq, which it wanted to do anyway. So Al Qaeda equally played into the neo-cons hands. It did the neo-cons work for it. So both sides have gotten their way. And where are we as a result of such a rampant fulfillment of strategic goals?
Similarly, Hamas provoked Israel to a violent reaction in Gaza, as a result of which Israel lost friends and credibility throughout the world, while ensuring the production of more terrorists with nothing to lose in Gaza. But when those terrorists strike, that will justify more actions designed to consolidate control over the West Bank and block the formation of a viable Palestinian state--just what the Israeli right wing wants. And where will that leave us?
Gandhi and other practitioners of non-violence like King, Mandela, Walesa, and others understood that to be provoked to violence plays into the hands of those who want to oppress you. The discipline of non-violence can break that cycle, saving the oppressor from himself, and you from the self you would become if you gave in to the cycle of violence.