You're four hours into a text argument. You're not sorry, and the fake apology, the "fine, sorry, whatever," would be a lie that settles nothing and teaches the other person that outlasting you works. But the fight is eating your whole day, your chest is tight every time the phone buzzes, and you can feel that no reply you send will be the one that ends it.
Here's the fact that unlocks this: text arguments don't end because someone wins. There is no winning reply. Each message you send is another hour of fight, because it demands an answer, which demands an answer. The argument is a machine that runs on replies, and both of you keep feeding it while wishing it would stop.
Which means ending it isn't about finding better words for your position. It's about closing the machine without surrendering your position, and those are separate acts. People conflate them, which is why they think their only options are apologize or keep fighting. The third option is to state where you stand, decline the medium, and stop:
I still see this differently than you, and I don't think either of us is going to type our way to an agreement. I'd rather talk about it in person this weekend when we're both calmer. I'm going to stop texting about it now, not because I'm dismissing you, but because this format is making us both worse.
Read what that does. No apology anywhere in it, your position is intact and stated. No new argument content, nothing for them to rebut. It names the real culprit, the format, which is generous and also true: text strips tone, rewards zingers, lets both people compose attacks at leisure, and never lets anyone see the other's face soften. And it announces the stop instead of just going silent, because silence mid-fight reads as a slammed door and generates three more furious messages, while an announced stop reads as a decision.
Then comes the actual test, which isn't the message. It's the next buzz. They will likely reply, possibly with something designed to be unignorable, a fresh accusation, a "wow, so you're just running away." The machine makes one last grab. If you answer it, everything above is undone and you've taught them that "I'm stopping" means "one more round." The discipline is: you said you're stopping, so you stop. If it helps, one closing line is allowed, once: "I meant it, this weekend. Not ignoring you." Then the phone goes down.
A distinction worth keeping sharp: refusing to fake an apology doesn't mean nothing is ownable. If somewhere in hour three you called them an idiot, you can own the conduct without conceding the argument, "I shouldn't have said that, and I still disagree with you," and we've written about that split in apologizing after a fight. But if there's nothing to own, don't manufacture it. A fake sorry isn't peace. It's a loan against the next fight.
You don't end a text argument by winning it. You end it by refusing to keep holding it, out loud, with your position still on its feet.