You don't have to win this one
"They're the one being stubborn"
Once the fact is disputed, there's a second thing you notice, which is that your partner won't budge. You've shown them the evidence. They're still saying Wednesday. That's not a disagreement any more. That's stubbornness, and stubbornness has to be pushed through.
Kathleen Kennedy and Emily Pronin, in 2008, studied what happens between people who disagree. Their first finding was that people see those who disagree with them as biased. Not wrong, biased, meaning their judgement is distorted by something. The second was that this perception drives how people then behave. Seeing the other person as biased, people took more conflict-escalating approaches to them, pushing harder, conceding less, treating them as someone to be got round rather than talked to. The third finding closed the loop. When the researchers manipulated people into seeing their adversary as biased, those people behaved more conflictually, and that behaviour made them look more biased and less worth cooperating with, to the other side. The researchers called it a bias-perception conflict spiral. You see them as biased, so you push. Your pushing makes you look biased to them, so they push. Round it goes.
Two people each sure the other's watch is wrong is a fair comparison for two sentences. Each one sets theirs more firmly, and neither looks at a clock.
Apply the spiral to the plumber. Your partner said Wednesday. To you, that's a person whose memory is distorted, probably by the recycling. So you produce the calendar with a certain edge, because you're dealing with someone stubborn. To them, the edge is the sign that you've stopped listening and started managing, which is what a biased person does. So they say "whatever", which is the concession that isn't one, and the temperature drops, and you both file the evening as the other one being difficult.
The point isn't that you're the stubborn one. It's that "they're the stubborn one" is what the spiral produces in both chairs, and that the sentence, once believed, is what makes the next move harder. Neither of you started the spiral. Both of you are in it. And the person who notices that first is the one who can step out, which is chapter 13's subject, and it doesn't require the other one to do anything at all.