There are some phrases that seem to be harmless and seem to make sense, but when you really look at what they mean they are truly an evil sentiment. The term "Cycle of Violence" is just such a term. Read this article
by Dr. Sowell. You will be enlightened.
Dennis Prager also deplores this phrase. It reminds him of how, even when he was young, he deplored this idea. Namely, if one student punched another student, then the student that was punched defended himself a teacher would come along let them know that they were both in trouble. We are doing the same when we call the retaliation of Israel a continuation of the "Cycle of Violence."
Now, I have some experience with this because as a father of three boys I have, on occasion, done exactly as the teacher in the above story. Two of my boys will yell downstairs that his brother has taken a toy that he was playing with. Of course both boys believe that they had the toy. So I take the toy away from both of them. This is a moral travesty, so why do I do it?
One reason is that I have no real way of determining which child is in the right. The other reason is simple moral laziness. The former reason is defensible, the latter reason is not.
In the case of Israel we do not have the excuse of not knowing who is in the right, and those that would morally equivalize Israel's actions are morally lazy.
Check out this article
by Dennis Prager to more fully understand what is going on.