Jess adds a point: different people express anger differently.
So we can't just assume that everyone else will express their anger the same way we would.
So how do you encourage an arena that allows for vigorous debate and sharing of ideas, without it degenerating into personal attacks and petty insults?
It's not that complicated. We're all human. We all say foolish, sometimes hurtful things without thinking them through (and sometimes we're annoyed enough to do it deliberately). We all have cultural blind spots, where ingrained habits may have problematic origins or consequences. We all mistakenly transfer habits and modes of interaction from one context to another, even when that may not be appropriate. We'll say things we don't mean because we're stressed about work, or an ill family member, or our pet just died. It happens, it's going to keep happening. We'll make other people angry, they'll make us angry.
We need to accept this (human nature: a thing), and we need to learn to adopt the many and varied techniques that have been invented to manage it.
We can set up safe spaces, where we suggest to people "only come here when you're able to interact in a calm, controlled manner". Not every space needs to be a safe space for everyone - the behaviour that's appropriate for a professional conference is going to be starkly different from that of an evening drinking and playing cards with your closest friends. What's entirely appropriate on a personal blog may be completely out of line on a shared collaborative mailing list.
We can create spaces to vent - to shout into the wilderness, whether anyone is listening or not.
The internet is, above all, a very human place. It allows us to connect, if ever so tenuously, across geographic and cultural boundaries that may have previously seemed insurmountable. We can, if we so choose, create a "filter bubble" where we only ever hear opinions that already agree with our own. But that's a choice - it's up to us. If we want, we can instead, dip into the cacophony, welcome the noise, and perhaps learn a little bit more of the invisible worlds that exist in parallel with our own every day, across the world, across town, and even across the street.
And if that means I have to get a little better at the arts of "agreeing to disagree" and even (gasp) "admitting I was wrong"? I'm still in :)
The main trick I personally use to avoid falling into those traps? If someone is angry at me, even if I don't yet understand why, I defend their right to be angry with me. If I ever find myself tempted to utter the following phrases, I know I've shifted to a mode of deliberately trying to troll someone rather than engage in a productive discussion:
(I will occasionally say the last one more constructively, but that's related to holding people in positions of power accountable for their words and actions)
While a lot of people pay lip service to the idea of "diversity of opinion", I sometimes wonder how many of them actually know what that looks like.
The world is a complicated place, and we're forced to navigate it without a cheat sheet that tells us "do such-a-such a thing to make yourself happy". There's no universally shared "meaning of life" (other than 42), so we're forced to muddle through, doing the best we can, based on the inadequate data we have.
That's loud, and noisy, and messy, and in the cacophony we may learn a little bit more about what it means to be human.
Yes, we have a right to say insensitive things (because giving the government coercive control over opinions is one of the most stupid things a citizenry can ever do, even while it makes sense to keep a tight rein on malicious deceit), but that comes part and parcel with the right of others to come back at us and point out our insensitivity.
It can be really, really hard to actually hear someone else's anger, especially when that anger is directed at ourselves, a friend, or someone we respect.
In particular, we often respond to the words, and get defensive about those, or (worse) we try to use mistakes in the words to argue against the reality of the anger. There are two major problems with such a literalist approach:
firstly, if someone is genuinely angry right now they're unlikely to be thinking clearly, and are hence unlikely to be choosing their words with careful precision. To argue with their precise wording, or to claim "you shouldn't be angry about that" is to completely miss the point of their anger, which is "you hurt me, and I am not happy". The thing they're superficially angry about is most likely a "straw that broke the camel's back" situation, rather than being the true cause of their anger. Asking "Why are you so angry?" is also an incredibly stupid thing to do at this point, because they probably don't know. "Why did that make me so angry?" is a question that can only be answered after you have had time to calm down and reflect on the situation a bit.
secondly, lashing back at anger with our own anger almost certainly means we weren't actually listening to what was said. When anger and hurt is met with anger and hurt, there's no more hope of productive dialogue than when anger and hurt is met with complete dismissal. In such situations, the onus is on the more powerful party to defuse the situation - anger and lashing out is primarily a tool for those that otherwise feel powerless. The more powerful party in an interaction generally doesn't need to rely on anger to get a reaction - they often have other tools at their disposal (if they didn't, then it would be an interaction between peers instead).
The other thing that literalist interpretations risk is to overreact to deliberately provocative statements. Doing so is a sign that you're operating out of sheer reflex - assuming that a barbed comment was meant literally, and then reacting disproportionately to it, rather than taking to the time to reflect on the nuance behind the words and understand what the speaker really meant.
So, we try to avoid anger, and we often try to avoid even witnessing anger. This can escalate to the point of wanting to deny other people's anger - to tell them "you shouldn't be angry about that".
There is often a reluctance to baldly state: "yes, I accept the reality of your anger, I just consider the pain I caused that triggered your anger to be a necessary, or at least acceptable, evil". I don't know where that comes from - I suspect it's a desire to see ourselves as "nice people", so we're reluctant to admit when others may have a legitimate reason to be angry with us.
I suspect the only reason I manage to avoid that reaction in most cases is that I don't suffer from any illusions about being fundamentally nice - my core mode of operation is to do what I think is, on balance and overall, right, rather than what "won't make other people angry". Even though my concept of "right" includes "default to respecting others", it also sometimes means being the "bad guy" that decides who wins, and who loses in a particular situation. When that happens, the folks that "lose" have legitimate cause to be angry with me, and I need to own that and accept it as a consequence of my actions.
Managing anger, our own and other people's, is a difficult thing.
Anger is scary - "I am acting without any concern whatsoever for the consequences" is disturbing, as it inherently breaks our theory of mind. You usually cannot predict the actions of someone that is genuinely angry as those of a rational agent, and when the prediction engine that is the human brain breaks down like that, it gets upset.
Anger can also be genuinely dangerous when coupled with the power to do harm (whether physical, social, financial, professional etc) to another.