A while back, I happened across the Atheism Resource's "Rational Debating" flow chart. The goal of this flow chart is to familiarize readers with rationality, and the chart is certainly useful in helping us reflect on how we can facilitate rational discussion. However, the termination points in this chart -- "This is not a discussion. I will not talk to you about this topic." and "You cheated. The discussion is terminated." -- are problematic, because they terminate discussion entirely, when the given rules of rational debating are not observed. This makes rational debating an ends, rather than a means.
This is dubious, because the goal of debate is uncovering and disseminating truths about the world we live in. Accordingly, it's unrealistic to believe we will arrive at truth by terminating irrational debate and participating solely in rational discussions, because humans are not consistently and persistently rational, and there's no reason to believe we ever could be. Rationality is not a final, general state humans arrive at, thereafter live in, and spread to others. No matter who we are or where we are, we will always encounter, and at various times produce irrational, unreasonable argumentation. Moreover, when we are successful in convincing someone of the superiority of an idea or claim, it's not only or primarily because we adhered to the rules of rational debating. There's a lot more to agreement than logic.
Consider the example of parents speaking to their children, whether those children are five, ten, fifteen, or twenty years of age, or older. By the paths of this flow chart, a parent must disengage when their child is being irrational, which can happen all the time, citing the judgment "This is not a discussion. I will not talk to you about this topic." This example highlights the problem of making rational debating an ends rather than a means: if the goal of debate is to uncover truth, then the idea that we should place a full stop on debate, before arriving at truth, is not rational.
Rather than terminating irrational debate, more realistic and more progressive endpoints for this flow chart might be something like "This is not a rational discussion. Let's talk about the rules of argumentation before we revisit this topic." and "Let's talk about first principles and fallacies, to see how we can both construct better arguments, and then we can try discussing the original topic again."
I know it can be hard work, carrying on discussion with someone who has told you nothing will change their mind, especially if they're always angry. We can only tolerate so much. But in my experience, if you give it time and keep trying, even raging bigots can turn around. I know this because I've kept irrational debates going, sometimes over months and sometimes over years, and I've seen change and progress in myself and others. This could not have happened if we cut our conversations off, rather than working to sort things out.
Ultimately, learning is impossible when we terminate discussion and disengage. This means we have to push the limits of what we can tolerate, to sustain dialogue. If we stop irrational conversations and tell people "the discussion is terminated," the only thing we're doing is halting the spread of rational discourse, thereby facilitating and fomenting irrationality in ourselves and others -- and doing that is, of course, irrational.