To err is human, but it still doesn't seem like most of us would like to admit our humanity. I hypothesize that a few different aspects that affect how readily you'll admit to having made a mistake:
- Whether you believe that you're the type of person who's honest and admits when they've made a mistake
- The subject area of the false statement - if it's one where you're fairly confident and competent, or not
- How confidently you claimed the false fact
- The severity of the error, how the mistake affects others
- Whether you discreetly can correct the problem
A few classmates and I were making a film for a high school project, where we needed to calculate something, perhaps 59 × 59. Me being an over-confident math whiz, I proceeded to calculate it in my head, arriving at 3661, at which point we used that value for the construction. The classmate responsible for (or rather capable of) editing the film, discreetly noted the error and removed me stating the result. Thanks, Martin!
It's only now, thirteen years later, that I have a large enough distance to the event, to tell the world about it. Even back then, I was probably the type of person who (sometimes) admits their mistakes, but the subject area (math) was one where I "never" made mistakes, especially not confidently, and the fact that we used the erroneous result for further construction made it seem more severe.
Oh, and I'm not at all ready to tell you about my mistake, triggering my writing this post.