"I might still be right"
Everything so far has assumed that at the turn you know. Often you do. But sometimes the turn isn't a switch to the other view. It's a loss of confidence in yours. You said the second exit, they said the third, they've mentioned the roadworks, and you're now genuinely unsure. You haven't been proved wrong. You've been made uncertain, and it feels as though the only two sentences available are "I'm right" and "you're right", and neither is true.
There's a third sentence, and this chapter is about giving yourself permission to say it. "I'm not sure any more." It isn't a climb-down and it isn't holding. It's an accurate report of where you are, and it's the most honest thing that can be said at that moment, because it's the only sentence that matches the inside.
Tenelle Porter and Karina Schumann looked at what makes disagreements go better, in four studies published in 2018, and the factor they examined was intellectual humility, which they describe as recognising the limits of what you know and appreciating what the other person knows. People higher in it were more open to hearing the other side's reasons during an imagined disagreement, and in a third study chose to read a larger share of opposing views when given the choice. "I'm not sure any more" is what that openness sounds like in a car. It's the sentence that lets the other person's roadworks into your account of the route.
Notice what it does to the argument. Holding says "the second is quicker" and waits to be proved wrong. The climb-down says "the third is quicker" and ends it. "I'm not sure any more" says "tell me about the roadworks," and the argument turns into a conversation about the route, which is what it should have been from the start. Nobody has lost. The line has been set down rather than dropped, and you can pick it up again if the roadworks turn out to have finished.
There's a version of this that runs through the whole book. You don't have to have a position on everything, and the positions you have don't have to be held at full strength. A view held lightly can be set down without a climb-down. A view held hard has to be dropped. Most of the roundabouts and suppliers and films in your week don't deserve the hard version, and if you hold them lightly to begin with, the turn arrives as a shrug.