God is a God of mercy. In fact, mercy is so much a part of his character that he expects his children to reflect him in this.
Just as God shows mercy to those who don't deserve it (us), he commands us to do the same. Jesus tells us to do good to and pray for those who hate and mistreat us. He concludes by saying:
"[L]ove your enemies, do good to them, and lend to them without expecting to get anything back. Then your reward will be great, and you will be sons of the Most High, because he is kind to the ungrateful and wicked. Be merciful, just as your Father is merciful. (Luke 6:35-36)
What kind of logic is this? This isn't the way the world works. It's divine wisdom, the "logic" of grace that doesn't make sense. As God showed mercy to us, he wants us to do likewise. This way, we'll reflect his character to the world around us and prove that we are his sons, because we'll be showing the family likeness.
This is so impossible and so contrary to human nature, that it can only be done by Jesus living in us. As we know his grace and forgiveness, we are freed to show the same lavish, undeserved kindness to those who hurt us.
What if I don't want to?
Well, there's a sobering and serious incentive to do so.
Jesus tells us how to pray in the so-called Lord's Prayer, which includes the petition: "Forgive us our debts, as we also have forgiven our debtors." Nice sentiment, right? Not quite. Jesus elaborates:
"For if you forgive men when they sin against you, your heavenly Father will also forgive you. But if you do not forgive men their sins, your Father will not forgive your sins." (Matthew 6:14-15)
Elsewhere in Scripture, it's put like this: "[J]udgment without mercy will be shown to anyone who has not been merciful. Mercy triumphs over judgment!" (James 2:13)
God is so serious about mercy, that he won't forgive us our sins if we withhold forgiveness from others.
Why?
Because we don't actually have the right to judge our brother, or to hold a grudge against him for what he has done to us. God is the only one who has the right to judge or to avenge. "Do not take revenge, my friends, but leave room for God's wrath, for it is written: "It is mine to avenge; I will repay," says the Lord. (Romans 12:19) Evildoers aren't getting away with it. They will face God's judgment—that is, if they don't repent. However, if we truly have God's heart, we would rather they repent than be judged. That's largely the point of showing mercy:
"On the contrary: 'If your enemy is hungry, feed him; if he is thirsty, give him something to drink. In doing this, you will heap burning coals on his head.' Do not be overcome by evil, but overcome evil with good." (Romans 12:20-21)
Our kindness serves the purpose of shaming the wrongdoer, softening his or her heart, showing him God's heart for him, and hopefully bringing him to repentance. But even if he never repents, we have still fulfilled our calling, and we know that he faces a far more serious penalty than we could ever deal out.
However, this can't simply be a show of kindness for the purpose of demonstrating what good, obedient Christians we are. God makes it clear our forgiveness must be real.
Jesus told a parable about a servant who was forgiven an unimaginable debt by his kind master. This servant then found a fellow servant who owed him a small amount of money, choked him, demanded he pay him back, and threw him into prison. The furious master then "turned him over to the jailers to be tortured, until he should pay back all he owed." (Matthew 18:34) Jesus appended this brief explanation: "This is how my heavenly Father will treat each of you unless you forgive your brother from your heart." (v.35)
This is hard. This is really, really hard. All we (I) can do, is to pray for God's grace and the ability to see as he sees, love as he loves, and show mercy with his strength. Repent when we are guilty of unloving, unmerciful thoughts or actions, and seek by God's help to be true sons who live out his heart. There's no other way, if we are to be followers of the living God.