You don't have to win this one
"If I let it go, I'm admitting they're right"
Here's the belief that makes the win feel compulsory. If you stop pressing, you've conceded. The only options are to win or to lose, and losing means agreeing to a thing that isn't true.
There's a third option, and the habit has hidden it. You can drop the fact without conceding it. Dropping isn't agreeing. It's declining to continue, and it says nothing about who was right.
Consider the plumber. You could say "you might be right, I'm not sure it matters", and nothing in that sentence is false. You might be right is true, in the sense that you haven't checked. I'm not sure it matters is true, in the sense that it doesn't. You haven't said the plumber came on Wednesday. You haven't said your partner was right. You've said the argument isn't worth having, which is an accurate statement about the argument.
The belief that dropping is conceding comes from imagining the argument as a contest with a scoreboard, where an unfinished round goes to the other side. That's how it feels from inside, and it's why chapter 1 named the score. But there's no scoreboard. There's a dinner table, and a fact about a plumber, and two people. The round doesn't go to anyone if nobody finishes it. It just ends, and the evening is still there.
There's also the question of what you'd be lying about. "Maybe it was Wednesday" would be a small lie if you were certain, and chapter 3 is about why you shouldn't be, without the calendar. "It doesn't matter" isn't a lie at all. It's the truest thing anyone says in the whole exchange. The plumber came. The job got done. The day is a detail, and saying so isn't surrender. It's proportion.
So the choice isn't between winning and losing. It's between winning, losing, and dropping, and the third one is the only one that doesn't cost the evening. Chapter 21 has the sentences. For now I'd just like you to notice that they exist, because the habit has spent years telling you they don't.