The only possible way of breaking a cycle of violence is for someone...eventually...not to hit back. This would apply to, for example, the longstanding problems in Ireland between Catholics and Protestants, the problems in the Middle East between Israel and various Muslims in that region, North and South Korea....and 2 or more individuals fighting verbally with each other on this forum.

It only ends when someone decides not to hit back.

The above doesn't apply to boxing, obviously, because boxing is entirely based on the premise of hitting back (until victory or the end of the round)...but it does apply to the wellnigh endless personal quarrels on this forum. They can only end when someone decides not to hit back.

Not hitting back can involve an actual act of goodwill...that is, forgiveness...mutual understanding...or just disengaging or ignoring or avoiding each other from that point on (if reacting in a positive way is just too much to bear...and for some, it is.)