“A person’s wisdom yields patience; it is to one’s glory to overlook an offense.”
Proverbs 19:11 

“Do not pay attention to every word people say, or you may hear your servant cursing you—for you know in your heart that many times you yourself have cursed others.”
Ecclesiastes 7:21-22

This may be difficult to accept, but more than likely we have all offended someone else at some point. You said or did something you shouldn't have, or said a quick comment in a way that came across as offensive. You talked about a co-worker behind their back and they found out what you said. You didn't invite someone to a party or you didn't show gratitude or appreciation when it was expected. In the same way, you have also probably been offended by someone else. They did one of these things to you and it left you feeling hurt, frustrated, or confused. The key here is to remember that we are often guilty of the same things that others have done to us, so with that in mind it is not unreasonable to remind ourselves that the way we would want others to treat us also works for how you would treat others. Would you want someone to hold a grudge against you for months or even years because of how you wronged them? Would you want them to hold bitterness against you and find a way to get back at you to somehow even the score? Or, would you want them to come to you so that whatever happened could be worked out and the relationship restored? In the same way you would want others to treat you, you should also treat others that way as well.

It is to your glory to overlook an offense. Don't dwell on it. Don't allow the offense to steal your joy, your peace, and the purpose that God has set before you. Don't allow the offense to be an excuse for you to abandon what is right and good. Don't gossip about that person or find a way to hurt them as they hurt you. Instead, we have an opportunity in this situation to be like Christ. To forgive the wrong, mend what is broken, and work to reconcile the relationship. A good way to think of offense is as a test. What will you do with the offense? Will it be a poison that affects many parts of you? Or, will the offense be fuel for you to do the right thing and restore that which was broken? Whenever you are offended, it's important to ask yourself and dwell instead on what you will do next, and if that planned response is Godly and pure, or if you have allowed one wrong to blossom into another.

Joyce Meyer chats in her podcast about offense and how we can combat the thief of offense, reroute offensive conversations, and even lean on the Holy Spirit for guidance and strength to be slow to speak and quick to listen.