You don't have to win this one
"They start it"
Fair enough. They said Wednesday first. They took the back road. They brought up Christmas. You didn't start any of it. You just responded, and the response got long.
Go back to the spiral. Kennedy and Pronin's account has no first move in it that anyone can see. You see their Wednesday as the start. They see your Tuesday, said with that certainty, as the start. Each of you is responding to a provocation the other one didn't know they'd made, and the spiral doesn't have an origin. It has two people each convinced they're the one responding.
Who started it is the least useful question in any argument, because it can't be answered and because it doesn't matter to the exit. The spiral can be left from either chair, at any point, by one person declining to make the next move. That person doesn't have to be the one who started it. It just has to be the one who noticed, and the one who noticed is the one reading this.
There's a cost to exiting first, and I'd name it honestly. It feels like losing. The other person said Wednesday and you said "you might be right, it doesn't matter", and it feels as though Wednesday has won. It hasn't. The fact hasn't changed. The plumber came when he came. What's happened is that the spiral stopped one turn earlier than it would have, and the evening survived. If that's losing, it's a kind of losing that leaves you with more than winning does.
And notice what happens on the other side of the table when you exit. Your partner, braced for the calendar, gets "you might be right" instead. Kennedy and Pronin's finding is that conflictual moves make the mover look biased. The opposite is also true. A conciliatory move, from someone who could have pressed, reads as fair, and a partner who sees you as fair is a partner who stops bracing. One exit doesn't end twenty years of spiral. Ten of them start to.