I've found that if someone is offended, if you react with openness and a willingness to listen to what they are saying, then the outcome will likely be positive.
If you are more concerned with defending yourself than listening to the other person, then it's likely the outcome is going to be negative.
This isn't rocket science. The problem is that people tend to react defensively. The only utility in such a reaction is a protection of your own ego. The irony is that in attempting to protect your own ego, you just end up making the situation worse, including for yourself.
Listening is a superpower.