Love Covers All Offenses

Proverbs 10:12 Hatred stirs up quarrels, but love covers all offenses.~ Sometimes when someone offends us we want to hurt them back instead of showing love. In 1 Corinthians 13:4 it says "Love is patient and kind. Love is not jealous or boastful or proud or rude." So when someone offends us or the people we are close to (family and friends) what are we to do? If we stay hating them it will only cause fights and quarrels, but love will cover all those offenses. Is that not what God has done for us? His love covered all of our offenses (sin) to Him. Through His death and resurrection we have been made right with Christ and all our offenses have been forgiven. Why should we not forgive the people that offend us when God has done so much for us?