You don't have to win this one
"If I'm wrong I'll admit it, so why can't they?"
Here's a belief that feels like fairness. You're not unreasonable. When you're wrong, you say so. You've admitted things. It's your partner who can't, and that's why the arguments run on.
Look at how often you're wrong, by your own account. Rarely, I'd guess, because you're careful, and you check, and you remember things. So the admissions are rare, not because you're stubborn but because the occasions are rare. That's how it looks from your chair. From theirs, it looks like a person who admits nothing and produces calendars, and who explains the rarity of their admissions by the rarity of their errors, which is exactly what Pronin's participants did. They saw a peer's self-serving account of a test result as biased and their own identical account as plain fact. "I'd admit it if I were wrong, I'm just not wrong very often" is a self-serving account, and it feels like accuracy, and it would feel like bias if your partner said it.
There's a second problem with the fairness argument, which is that it's a move in the spiral. "I'd admit it, why can't you" is a claim about the other person's character, made in the middle of a disagreement about a plumber, and Kennedy and Pronin's finding is that treating the other person as the biased one is what makes them dig in. You've stopped arguing about Tuesday and started arguing about whether they're the kind of person who can admit things, and nobody has ever conceded a date in order to prove they're not stubborn.
And there's what your admissions have looked like, on the occasions they've happened. In my observation, people who argue to be right admit error in a particular way, which is fast, complete and slightly grand, so that the admission itself becomes a small demonstration of character. "You're right, I was wrong, I hold my hands up." That's a good sentence and it's also a way of being right about being wrong, and partners notice.
The test isn't whether you'd admit it. It's whether you drop the ones you can't check. A person who says "you might be right" about the things nobody can know is a person whose rare admissions of error will be believed when they come. A person who only concedes when the calendar forces it has taught their partner that concessions are extracted, not offered, and will find their own extracted in return.