From where do we know that it is cruel to not forgive? For it says, "Abraham prayed to G-d and G-d healed Abimelech..." (Bereishit (Genesis) 20:17).Mishna in Baba Kamma 8:7
Jewish Law (Halacha) requires one to ask forgiveness from anyone whom you may have harmed whether the harm was physical, financial, emotional, or social. Also, one is required to be gracious in granting forgiveness.
The Rambam in Hilchot Teshuvah (Laws of Repentance) 2:9-10, writes:
Repentance and Yom Kippur only atone for sins between Man and G-d such as eating forbidden foods or engaging in forbidden sexual
relations. Sins between one man and his fellow, such as striking, cursing, or robbing are never forgiven until one pays up his debt
and appeases his fellow. Even if he returns the money he owes he still must ask for forgiveness. Even if he only spoke badly about
him he must appease and beseech until he is forgiven. If his fellow refuses to forgive him then he must bring a group of three of his
friends (presumably the injured party's friends) and go to him and ask him [for forgiveness]. If he still does not forgive him he must
go to him a second and third time (with three other people). If he still refuses to forgive him he may cease and the other is the sinner.
If [the injured party] is his teacher (rebbe) he must go to him even a thousand times till he is forgiven.
It is forbidden to be cruel and difficult to appease, rather, a person must be quick to forgive and difficult to anger and when the sinner
asks for forgiveness he should forgive him willingly and wholeheartedly....
The Shulchan Aruch, Orech Chaim 606:1 in the Laws of Yom Kippur, says essentially the same thing adding that one may withhold forgiveness if it is for the good of the person asking. It may be appropriate to withhold forgiveness to teach the supplicant not to take it lightly. Withholding forgiveness may also be permitted when someone spread false rumors about you but then it says that in such a case one should still forgive.
The prayer before Kol Nidrei on Erev Yom Kippur says:
I extend complete forgiveness to everyone who has sinned against me, whether physically or monetarily, or spoke lashon hara about me or even false
reports. And also for any damages, whether on my body or my property and all sins between a man and his fellow except for money which I can claim in
a court of law and except for someone who sins against me saying, "I will sin against him and he will forgive me". Except for these I grant
complete forgiveness and no person should be punished on my account. And just as I forgive everyone so should You grant me favor in the eyes of all
men that they should completely forgive me.