As humans we are imperfect. We make mistakes, we fail and we inevitably disappoint one another. Because of this, we need forgiveness. We should forgive others, because we would want others to forgive us. Put yourself in the position of the other person. If you were them, if you made the same mistake, would you want forgiveness? Forgive others, just as you would want to be forgiven.
“Bear with each other and forgive one another if any of you has a grievance against someone. Forgive as the Lord forgave you.” – Colossians 3:13