I agree with the general point but I don't think it's best to contrast getting offended with staying calm. The way I imagine offense happens is that we classify somebody's actions or beliefs as harmful to us or our group and that makes us annoyed, we then automatically decide that the best way of fixing the situation is to destroy the other person's ability to cause us harm and if we lack any other option of doing that we default to politics as our means of attack.
And then that switch gets flipped in our heads that puts us in a mode of thinking more adapted to lowering someone's social standing. This last step specifically is what I think of when I hear about 'getting offended'. If you resist flipping the switch your unfavorable assessment of the situation will remain. You will still be annoyed at the fact that there's someone who seems to be a social threat (but at least you won't feel compelled to exaggerate the threat for the sake of better drama). It seems like dealing with annoyance should be a separate skill from not going off into narratives about how you are inherently more virtuous than the enemy. So rather than trying to stay completely calm as an alternative to getting offended, maybe it's better to focus on the minimal change that would stop us from turning into raging monkeys while still possibly leaving us annoyed humans. This might also be more palatable to people who get offended upon hearing advice not to.
Related to: Politics is the Mind-Killer, Keep Your Identity Small
Followed By: How to Not Get Offended
One oft-underestimated threat to epistemic rationality is getting offended. While getting offended by something sometimes feels good and can help you assert moral superiority, in most cases it doesn't help you figure out what the world looks like. In fact, getting offended usually makes it harder to figure out what the world looks like, since it means you won't be evaluating evidence very well. In Politics is the Mind-Killer, Eliezer writes that "people who would be level-headed about evenhandedly weighing all sides of an issue in their professional life as scientists, can suddenly turn into slogan-chanting zombies when there's a Blue or Green position on an issue." Don't let yourself become one of those zombies-- all of your skills, training, and useful habits can be shut down when your brain kicks into offended mode!
One might point out that getting offended is a two-way street and that it might be more appropriate to make a post called "Don't Be Offensive." That feels like a just thing to say-- as if you are targeting the aggressor rather than the victim. And on a certain level, it's true-- you shouldn't try to offend people, and if you do in the course of a normal conversation it's probably your fault. But you can't always rely on others around you being able to avoid doing this. After all, what's offensive to one person may not be so to another, and they may end up offending you by mistake. And even in those unpleasant cases when you are interacting with people who are deliberately trying to offend you, isn't staying calm desirable anyway?
The other problem I have with the concept of being offended as victimization is that, when you find yourself getting offended, you may be a victim, but you're being victimized by yourself. Again, that's not to say that offending people on purpose is acceptable-- it obviously isn't. But you're the one who gets to decide whether or not to be offended by something. If you find yourself getting offended to things as an automatic reaction, you should seriously evaluate why that is your response.
There is nothing inherent in a set of words that makes them offensive or inoffensive-- your reaction is an internal, personal process. I've seen some people stay cool in the face of others literally screaming racial slurs in their faces and I've seen other people get offended by the slightest implication or slip of the tongue. What type of reaction you have is largely up to you, and if you don't like your current reactions you can train better ones-- this is a core principle of the extremely useful philosophy known as Stoicism.
Of course, one (perhaps Robin Hanson) might also point out that getting offended can be socially useful. While true-- quickly responding in an offended fashion can be a strong signal of your commitment to group identity and values[1]-- that doesn't really relate to what this post is talking about. This post is talking about the best way to acquire correct beliefs, not the best way to manipulate people. And while getting offended can be a very effective way to manipulate people-- and hence a tactic that is unfortunately often reinforced-- it is usually actively detrimental for acquiring correct beliefs. Besides, the signalling value of offense should be no excuse for not knowing how not to be offended. After all, if you find it socially necessary to pretend that you are offended, doing so is not exactly difficult.
Personally, I have found that the cognitive effort required to build a habit of not getting offended pays immense dividends. Getting offended tends to shut down other mental processes and constrain you in ways that are often undesirable. In many situations, misunderstandings and arguments can be diminished or avoided completely if one is unwilling to become offended and practiced in the art of avoiding offense. Further, some of those situations are ones in which thinking clearly is very important indeed! All in all, while getting offended does often feel good (in a certain crude way), it is a reaction that I have no regrets about relinquishing.
[1] In Keep Your Identity Small, Paul Graham rightly points out that one way to prevent yourself from getting offended is to let as few things into your identity as possible.