Socially: Admitting you were wrong makes you look incompetent. If you were wrong then, why should anyone listen to you now?
Physiologically: Changing ingrained opinions on which many others are formed probably requires a good deal of brain re-wiring and may require solid plasticity. I'm unsure how much of a problem this is for the brain.
I guess there are a lot of other costs, but I can't come up with more.
> Admitting you were wrong makes you look incompetent.
It certainly makes you feel like you look incompetent. I wonder how much it makes others judge you as incompetent. Perhaps this issue has been researched? (I'm guessing that it might matter a great deal how one was wrong; there are different ways to be wrong, and different levels of wrongness.)
Many of the terms we associate with "the end of the world" have meanings which amount to "revealed truth": revelation, apocalypse, enlightenment, catastrophe.
The upshot of each is that your previous understanding of the world is overthrown. It's not so much that it's the world which has ended as your worldview.
Mental models are difficult and expensive to construct. It takes an entire childhood and adolescence for humans, arguably a fair bit of adulthood as well.
Leaving those comfortable confines, even where they're wrong, is pretty distressing. We'll often work hard to re-shoebox reality into models to which it fits at best poorly instead.
Usually there is a reason people believe what they believe. It's called motivated reasoning. For instance I know my religion is full of shit, but it's a very important part of my identity. Therefore I must find reasons to continue to believe in it and defend ideas that it puts forward.
Well lets take this into the extreme. Lets assume you adopt a new opinion that a life is only worth it's economical value. The amount of mental work to integrate that believe in your current set of opinions (by changing them) is huge. So you'd rather not do it.
Another example: the lie your company is on a good path. Knowing accepting it is on a bad path, means a lot of work.
Perhaps there is some real cost to changing your opinion. What is that cost, and how can it be lowered? Or raised, for that matter?