"I've said it now, I have to see it through"

You said it with some force. You may have said it twice. There's a feeling that having invested that much in the line, the investment obliges you, and that climbing down now would waste everything you've already said.

This is an old and well-studied trap, and it has a name. Barry Staw described it in 1976 as escalating commitment to a chosen course of action. In a 1977 follow-up with Frederick Fox, the two summarised the earlier finding, that people were most likely to keep pouring resources into a failing course when they'd been personally responsible for the bad outcome so far, and found the effect again in the short term, though it faded as time went on. Dustin Sleesman and colleagues gathered the research in a 2012 meta-analysis of the many things found to drive it. The mechanism, put plainly, is that having chosen something that's going badly, people put more in rather than less, because putting more in feels like the only way to make the earlier choice come right.

An argument is a small version of this. The sentences you've already said are the investment. The turn is the moment the investment is revealed to be failing. And the next defence, the one about the roadworks nearly being finished, is you putting more in. The more you've said, the more it feels like there is to lose, and so the longer you hold.

Here's the thing about what you've already said. It's gone. Nothing you say next can make the earlier sentences true, and nothing you say next can get them back. If you've paid for a cab to the wrong address, the fare's spent whether you get out or sit there while the meter runs. The only question left is whether you want to keep paying.

The climb-down doesn't waste what you've said. What you've said was wasted at the turn, when it turned out to be wrong, and there's nothing to be done about that. What the climb-down does is stop the meter. Every sentence of holding after the turn is a new sentence that's also wrong, and those are the ones you've still got a choice about.