Every virtue is an expression of love. Richard P. McBrien, Catholicism. Revenge merely sets one on the same level as the one who has wronged you, forgiveness moves you both closer to God. From forgiveness it is a tiny step to accept others as beloved children of God, and to love them as such. Forgiveness is seeing others as loved as equally as we are by God, and as justified, forgiven and reconciled by the blood of Jesus as we are.
Forgiveness removes our rights to avenge and to revenge.
It prevents us from attacking others. Forgiveness costs - often it seems to produce more pain than the original wounding. It involves accepting voluntarily the harm or evil that has been inflicted on oneself, and letting the other person go free. In love, we bear the cost of those sins against us. Both human and divine forgiveness are substitutional.