When we "go after" those who hate or hurt us, we're engaging in the very behaviors we find so offensive; it doesn't help anything good happen.
Besides that, by patiently enduring the nastiness others throw our way, we may actually learn how we have been wrong as well as wronged.
If we have attempted reconciliation and understanding to no avail, it's better to simply place the offending party in God's hands and move on with our lives.
I'd advise reading all of Psalm 37. It's a treasure trove of insight and inspiration!
1Do not fret because of the wicked; do not be envious of wrongdoers,
2for they will soon fade like the grass, and wither like the green herb.
3Trust in the Lord, and do good; so you will live in the land, and enjoy security.
4Take delight in the Lord, and he will give you the desires of your heart.
5Commit your way to the Lord; trust in him, and he will act.
6He will make your vindication shine like the light, and the justice of your cause like the noonday.
7Be still before the Lord, and wait patiently for him; do not fret over those who prosper in their way, over those who carry out evil devices.
8Refrain from anger, and forsake wrath. Do not fret—it leads only to evil.
9For the wicked shall be cut off, but those who wait for the Lord shall inherit the land.
10Yet a little while, and the wicked will be no more; though you look diligently for their place, they will not be there.
11But the meek shall inherit the land, and delight themselves in abundant prosperity.
12The wicked plot against the righteous, and gnash their teeth at them;
13but the Lord laughs at the wicked, for he sees that their day is coming.
14The wicked draw the sword and bend their bows to bring down the poor and needy, to kill those who walk uprightly;
15their sword shall enter their own heart, and their bows shall be broken.
16Better is a little that the righteous person has than the abundance of many wicked.
17For the arms of the wicked shall be broken, but the Lord upholds the righteous.
18The Lord knows the days of the blameless, and their heritage will abide forever;
19they are not put to shame in evil times, in the days of famine they have abundance.
20But the wicked perish, and the enemies of the Lord are like the glory of the pastures; they vanish—like smoke they vanish away.
21The wicked borrow, and do not pay back, but the righteous are generous and keep giving;
22for those blessed by the Lord shall inherit the land, but those cursed by him shall be cut off.
23Our steps are made firm by the Lord, when he delights in our way;
24though we stumble, we shall not fall headlong, for the Lord holds us by the hand.
25I have been young, and now am old, yet I have not seen the righteous forsaken or their children begging bread.
26They are ever giving liberally and lending, and their children become a blessing.
27Depart from evil, and do good; so you shall abide forever.
28For the Lord loves justice; he will not forsake his faithful ones. The righteous shall be kept safe forever, but the children of the wicked shall be cut off.
29The righteous shall inherit the land, and live in it forever.
30The mouths of the righteous utter wisdom, and their tongues speak justice.
31The law of their God is in their hearts; their steps do not slip.
32The wicked watch for the righteous, and seek to kill them.
33The Lord will not abandon them to their power, or let them be condemned when they are brought to trial.
34Wait for the Lord, and keep to his way, and he will exalt you to inherit the land; you will look on the destruction of the wicked.
35I have seen the wicked oppressing, and towering like a cedar of Lebanon.
36Again I passed by, and they were no more; though I sought them, they could not be found.
37Mark the blameless, and behold the upright, for there is posterity for the peaceable.
38But transgressors shall be altogether destroyed; the posterity of the wicked shall be cut off.
39The salvation of the righteous is from the Lord; he is their refuge in the time of trouble.
40The Lord helps them and rescues them; he rescues them from the wicked, and saves them, because they take refuge in him.