The person who says they were wrong has chosen a more useful future over a more comfortable story.

Admitting a mistake costs something specific: the version of events in which you were sensible all along. People hold onto that version because it is comfortable and because it protects how others see them, and the price is that they keep operating on a picture they know to be false. Saying it out loud trades the comfortable account for an accurate one, which is the only kind you can plan from.

If you have been defending something you no longer believe, say the plain sentence and skip the long explanation. When someone else does it, receive it without extracting a further apology.