Forgiveness is a hard concept for many of us to grasp, but is directly linked with our well-being. When we let negative things fester and eat away at us, we are not allowing goodness to come in. We aren't opening our hearts and minds to the chance of peace.
When someone has done us wrong, we can either choose to forgive them or not. Even if they are not sorry or do not necessarily deserve our grace, we can still grant it to them. Why would I forgive someone who isn't sorry? Isn't that like giving them a free pass to treat you badly again? No, it's actually a chance for you to be forgiven. What? But I did nothing wrong? Why should I be forgiven? Matthew 6:14-15 reads: "For if you forgive men their trespasses, your heavenly Father will also forgive you. But if you do not forgive men their trespasses, neither will your Father forgive your trespasses." Jesus paid the price for our sins against Him even though we totally did not deserve it. That is some overwhelming grace. So, those who are following in Christ's footsteps, must act accordingly, regardless of how hard it may be. Someone doesn't have to deserve your grace in order to receive it. At this point, it's not even about the one who has wronged you. It's about your relationship with God. Christ is pleased when we forgive others, as He has forgiven us.
So even if you don't think you should forgive someone in order to please God, at least do it for yourself. If you fill your life with anger and resentment, where is there room for happiness? You may be hurt by someone you love, but you cannot enjoy your relationship with them until you have forgiven them. Even if there isn't a chance for repair, by granting them grace, you are allowing yourself to be at peace.