When I was a teenager, I picked up my mom's copy of Dale Carnegie's How to Win Friends and Influence People. One of the chapters that most made an impression on me was titled "You Can't Win an Argument," in which Carnegie writes:
Nine times out of ten, an argument ends with each of the contestants more firmly convinced than ever that he is absolutely right.
You can’t win an argument. You can’t because if you lose it, you lose it; and if you win it, you lose it. Why? Well, suppose you triumph over the other man and shoot his argument full of holes and prove that he is non compos mentis. Then what? You will feel fine. But what about him? You have made him feel inferior. You have hurt his pride. He will resent your triumph. And -
"A man convinced against his will
"Is of the same opinion still."
In the next chapter, Carnegie quotes Benjamin Franklin saying how he had made it a rule never to contradict anyone. Carnegie approves: he thinks you should never argue with or contradict anyone, because you won't convince them (even if you "hurl at them all the logic of a Plato or an Immanuel Kant"), and you'll just make them mad at you.
It may seem strange to hear this advice cited on a rationalist blog, because the atheo-skeptico-rational-sphere violates this advice on a routine basis. In fact I've never tried to follow Carnegie's advice—and yet, I don't think the rationale behind it is completely stupid. Carnegie gets human psychology right, and I fondly remember reading his book as being when I first really got clued in about human irrationality.
It's important that people's resistance to being told they're wrong is quite general. It's not restricted to specific topics like religion or politics. The "You Can't Win an Argument" chapter begins with a story about a man who refused to accept that the quotation "There's a divinity that shapes our ends, rough-hew them how we will" came from Hamlet rather than the Bible. Carnegie correctly identifies the reason people can be irrational about such seemingly unimportant questions: pride.
In fact, if Carnegie's book has one overarching theme, it's the incredible power of the human need to think highly of ourselves (individually, not as a species). It opens with stories of a number of gangsters who insisted against all evidence that they were good people (including Al Capone, and a couple of now-forgotten names that were contemporary references at the time the book was written in 1936). By the end of that first chapter, those examples have been spun into what I suppose was intended to be a positive, upbeat message: "Don't criticize, condemn, or complain."
It had the probably unintended effect, though, of helping to give me a deep cynicism about human nature, a cynicism which persists to this day. In particular, I saw in a flash that what Carnegie was saying implied you could get people to support some deeply horrible causes, as long as you presented the cause in a way that told them how wonderful they are. I think I even had an inkling at the time that there was some evolutionary explanation for this. I can't claim to have exactly derived Robert Trivers' theory of self-deception on my own, but I certainly was primed to accept the idea when I got around to reading Steven Pinker in college.
(Around very roughly the same time as I read How to Win Friends and Influence People, I read Homer's epics, which served as the other early building block in my present cynicism. It was Homer who taught me there had once been a culture that held that raping women taken captive in war was a perfectly normal thing to do, even suitable behavior for "heroes.")
But such cynicism is a post for another day. When it comes to rationality, the effect of Carnegie's book was this: even after having read all of the sequences and all of HPMOR, I still think that the human need to think highly of ourselves is a far more important source of human irrationality than oh, say, the fundamental attribution error or the planning fallacy. It does seem foolish to be so strongly influenced by one book I read in my early teens, but on the other hand the evidence I've encountered since then (for example learning about Trivers' theory of self-deception) seems to me to confirm this view.
So why do I go on arguing with people and telling them they're wrong in spite of all this? Well, even if nine times out of ten arguing doesn't change anyone's mind, sometimes the one time out of ten is worth it. Sometimes. Not always. Actually, with most people I'm unlikely to try to argue with them in person. I'm much more likely to argue when I'm in a public internet forum, when even if I don't persuade the person I'm directly talking to, I might persuade some of the lurkers.
Now there are various tactics for trying to change people's minds without directly telling them they're wrong. Bryan Caplan's The Myth of the Rational Voter has a section on how to improve undegraduate economics classes, which includes the observation that: "'I'm right, you're wrong,' falls flat, but 'I'm right, the people outside this classroom are wrong, and you don't want to be like them, do you?' is, in my experience, fairly effective." Of course, this doesn't work if the other person has definitely made up their mind.
There's also the Socratic Method, which Carnegie sings the praises of. I think many people get the wrong idea about the Socratic method, because the most famous source for it is Plato's dialogues, which are works of fiction and tend to have things go much better for Socrates than they ever would in real life. From reading Xenophon's Memorabilia, my impression is that the historical Socrates was probably something of a smartass who was not very good at winning friends or influencing most of his immediate contemporaries. (They did vote to kill him, after all.)
There may be a version of the Socratic method that's more likely to actually make progress changing people's minds. I recently read Peter Boghossian's A Manual for Creating Atheists, a how-to book for atheists who want to get better at talking to believers about religion. Boghossian's approach is heavily inspired by Socrates, and the examples of conversation he gives, based on actual conversations he's had with believers, are far more believable than Plato's—indeed, I'm left wondering if he used a tape recorder.
What most stands out about those conversations is Borghossian's patience. He politely keeps asking questions as the conversation seemingly goes round in circles, sometimes even shutting up and listening as his interlocutors spend several minutes basically repeating themselves, or going off on a tangent about the leadership structure of their church.
I bet Borghossian's techniques are great if you have the time and patience to master and apply them—but you won't always have that. So while I recommend the book, I don't think it will always be an alternative to sometimes straight-up telling people they're wrong.
Oh, and then there's just plain oldfashioned trying to be polite and direct at the same time. But that doesn't always work either. As Daniel Dennett once said, "I listen to all these complaints about rudeness and intemperateness, and the opinion that I come to is that there is no polite way of asking somebody: have you considered the possibility that your entire life has been devoted to a delusion?"
In spite of all this, there's still a tradeoff you're making when you criticize people directly. I've known that for roughly half my life, and have often made the tradeoff gladly. I tend to assume other rationalists know this too, and make the tradeoff consciously as well.
But sometimes I wonder.
How many people on LessWrong realize that when you tell someone their AI project is dangerously stupid, or that their favorite charity is a waste of money, you risk losing them forever—and not because of anything to do with the the subtler human biases, but just becasue most people hate being told they're wrong?
If you are making a conscious tradeoff there, more power to you! Those things need saying! But if you're not... well, at the very least, you might want to think a little harder about what you're doing.