An eye for an eye makes the whole world blind. --Ghandi
Tit for tat is not equivalent to an eye for an eye. It is not even equivalent to "Do unto others as they do unto you" (the "Brazen Rule"), which is "repay evil with evil" + "repay kindness with kindness". Tit for tat means "be cooperative at first, then do to others what they do to you". Game theory shows that this principle, when consistently applied, reaches the most desirable outcome for everyone, e.g. in the iterative Prisoner's Dilemma.
Tit for tat implies being willing to forgive and forget. I try to apply this principle whenever possible.
Regards,
Erik