I usually welcome a correction (especially on something important) but when I am annoyed by corrections here are some reasons why (could be any subset of these in any given example):
1) A more important thing is being interrupted by a less important thing. (I'm in the middle of explaining something complicated and you're interrupting to correct a mispronounced but perfectly clear word?!)
2) The "error" isn't actually wrong (lots of grammatical stuff falls into this category, like split infinitives and using "they" to mean 3rd person singular ungendered).
2b) The "correction" is a misunderstanding of what I'm saying. If what I'm saying doesn't make sense to you, why not be charitable and assume I must mean something else, rather than assuming that you don't understand because it's wrong?
3) It offends my pride to find out that I am wrong. (I don't endorse this one, just noting that it happens to me.)
Correcting in the form of a question does a lot to help with 2 and 3, 2 because it doesn't assume I'm the one in the wrong, 3 because it allows me to retain agency and be the one to determine that I've made an error, which is less humiliating than submitting to the superior judgment of someone else.
1a. Do you also get offended when a book/wikipedia tells you you're wrong?
1b. Would you get offended when a book chapter has a sidebar: "Some ignorant people believe X, which is in contradiction with chapter 1" when you, of course, happen to believe X?
2: Does your pride get offended when you're talking in a group and a person standing next to you is corrected for a belief you hold as well?
3a. You google a question and come across a Quora question that exactly explains your position the way you would have written it. The position is then exposed a...
The sequences cover the virtue of admitting you've made a mistake. We all make mistakes and when we do we ought to say oops and move on. I was taught this at an early age and I grew up in an environment where admitting error had no social stigma and where correcting somebody (even in public) was commended. Good times were had by all.
Needless to say, I eventually came into contact with the real world and I had to change my behavior. For instance, correcting somebody's pronunciation used to result in immediate repetition of the correct pronunciation followed by "thanks" and the discussion would continue without interruption. Or just a simple nod to acknowledge the correction. In the adult world a correction results in an annoyed look or a glare instead.
So it turns out that some people, highly intelligent and intellectual people, seem to be completely unable to admit error. Even when it concerns a trivial mistake, such as getting a factoid wrong, the best response I can hope for is a grunt of acknowledgement. I'm not talking about uneducated or intellectually insecure people here.
Okay, so a lot of adults don't appreciate being corrected. Duly noted. I could move on, but the virtues of scholarship and curiosity compel me to find out why. Predictably Irrational (Ariely) and Influence (Cialdini) don't have the answers. My non-scientific experiments indicate that prefacing a statement with "That's wrong because..." doesn't work. It seems to make people extra defensive. Standard strategies of persuasion do work, of course. Rephrasing the correction as a question? Works. Saying "Hmm" and pausing before you correct? Works. Making a suggestion that indirectly points out the mistake? Yep, works. These are all standard strategies of persuasion and they can be used to work around the issue but they don't explain why it is that some people have such an aversion to being corrected in the first place.
So where does the aversion come from?
In a group context signaling could explain it: when you correct somebody you draw attention to a mistake and this could lead to (perceived) loss of status. I don't think this is the real cause because people seem equally annoyed when corrected in a private conversation where there is nobody to signal towards. In cases where signaling takes a dominant role (e.g. when a bunch of guys are talking and a woman joins in) you clearly see a change in behavior because the guys wish to be perceived in a specific way. So in some groups signaling effects can make it more difficult to admit error but signaling is not the underlying cause that makes people averse to acknowledging mistakes in the first place.
Maybe it is an issue of ego. Is a correction seen as the role of a teacher thereby forcing the other in the student role? That would explain the aversion, but if that's the explicit thought process otherwise rational people would see it doesn't make sense and change their behavior accordingly. So there can't be an explicit (tactical) thought process underlying the behavior at all!
Maybe people don't wish to admit their mistake because they prefer to keep it all ambiguous. By admitting a mistake they know I know that they know they're wrong (youtube). This feels like the most plausible explanation, even though the explicit admission of the mistake does not change the state of the shared knowledge: the situation wasn't really ambiguous to start with.
So then I'm forced to conclude it's some knee-jerk, gut level aversion to being corrected that has no underlying logic or motivation. I cannot even begin to comprehend this. Given the effort required to find and correct (cognitive) mistakes how can we feel anything but gratitude when somebody points out where we go wrong?
Can somebody who has (or had) this aversion to admitting mistakes explain it in terms I can understand?