I have spent a lot of time over the last two or three decades thinking about things such as emotion. I am, I think, more aware of how emotion works on the mind, behavior, and beliefs than most. I have much that I could still learn, but I feel like I have some understanding (dare I say ‘wisdom’?) worth paying attention to on the subject.
In the times when I have been most offended, defensive, and have pulled (or ran) away from something I did not like or want to hear, I have found that all that resulted was an overall loss. The times when my inability, unwillingness, and fear of facing a challenge and trying to find out why I was offended was never a victory.
There are certainly times when an offending action leaves you with the wise course of simply walking away. There are times when offense has nothing to teach us. But there are other times when offense can be a great teacher, and we need to practice in order to tell the difference between the two. And it is quite easy to be wrong, so I tend to lean towards introspection in all cases of offense, disagreement, or even dislike of another idea or person.
If you are offended, even if you must walk away (if only temporarily), make sure to at least reflect on it. Be sure that the cause of the offense is not something rubbing against a fear, insecurity, or where you may simply be wrong.
In short, running or walking away from offense can be a way to hide from your potential to learn about yourself. Others, when they offend you, may have something to offer you. Be not deceived by offense; for it can often be a gateway to self-knowledge.