...comes from the wonderfully cantankerous early 20th century actor W.C. Fields:
I don't have to attend every argument I'm invited to.
We're so quick to assume that if someone has an issue or a dispute or wants to pick a fight with us for some reason that we're obligated to reciprocate. "We've been invited to an argument," we say to ourselves, "and it would be rude to decline."
We would do well to reconsider that logic.
I'm not suggesting that we should be callous--just the opposite. When someone's upset with us, we should always respond with empathy and curiosity, at least initially. But that stance doesn't obligate us to take any subsequent action whatsoever. Meeting an argument with empathy and curiosity actually makes it easier to decline to attend, should we conclude that we have better things to do.
Sometimes declining to attend an argument means that we disengage and move on. Sometimes it takes the form of a joke that puts a leak in the balloon of the other party's outrage. Another option, though, is simply stepping aside.
We don't have to bear the brunt of someone's anger or frustration, should we conclude that it's unwarranted, and that doesn't mean we have to stop interacting with them. We can step aside, let the freight train pass, and then continue the conversation
We don't have to respond to a hostile question or one asked in bad faith, and that doesn't mean we have to end the dialogue. We can step aside and answer a different, better question--the one that should have been asked but wasn't.
Of course, this is easy to discuss at a remove and hard to do when facing someone who very much wants us to accept their invitation to argue. The key, as always, is emotion management: Reframe the situation, acknowledge and attune to our emotions, and build our capacity for mindfulness (topics discussed further here, here and here.)