Why you should admit your mistakes

In the book Yes!: 50 Scientifically Proven Ways to Be Persuasive, the authors explain why it's not a good idea to hide your mistakes. They say "...this strategy is likely to be ineffective because it does nothing to prove to skeptics that we have any control over the problem or that we have the ability to fix the problem."

And when mistakes are discovered by others, it's easy for them to wonder what additional "deceptive impulses" may occur in the future. In other words, they'll have a harder time trusting you.