Because they believe they will (feel) better.
They want to see the offenders punished or hurt in some way. No one likes to be bullied or taken advantage of. Whether someone goes through the legal channels or physically strikes back their motivation is the same. They don't want to be anyone's doormat.
Instinctively for most of us when we get hit we hit back.
Very few people are going to simply walk away and allow "karma" to avenge them. We've been taught: "You have to stand up to bullies."