1. Eastern wisdom advocates that revenge is futile.
2. Why waste human resources on revenge when nature sets things right according to its own natural order of things?
3.The person who has erred against Dharma(Universal, Natural Law) has already committed a wrong. Why join him/her and suffer a similar fate by repeating his/her actions?
4.Focus on what 'needs' to be done (damage control & prevention of the same in the future) and not on what you 'want' done (taking revenge).
5.This attitude also prevents the thinker from doing a similar crime as the wrong doer in the future.
6. Revenge harbors hate, a negative emotion which has its own cause and effects. Hate consumes.
7. Violence in some form also involved.
8. Leads to inner introspection and higher evolution through abstention from violence, forgiveness but not forgetfulness.
9. Letting the past rest and living in the present without harboring/carrying negative emotions into the future.
Taking revenge is allowed in Islam, but Islam encourages forgiveness for the sake of Allah. He promises a reward for it, either in this world or in the Hereafter. Forgiving others not only brings inner peace but also strengthens faith and patience.