My uncle is an entrepreneur-turned-corporate executive and has achieved considerable career success in his life, which is just to say that he's imposing and has a track record of getting what he wants.
One summer between my junior and senior years of college he hired me to help landscape his lawn. Several weeks after I had started, I made a small mistake.
"Oh, sorry about that, I'll just --"
"George, never say you're sorry" he said.
"Sure, I just meant that --"
"I know what you meant, but never say sorry, it makes you appear weak. Instead of saying you're sorry, fix the problem." He paused for a moment, looking at me, and then went back inside.
His advice ran so counter to what I had been taught that it stuck in my memory. I had always been taught to admit mistakes and correct them, but here he was suggesting I skip the first step. I'm still not sure I agree with it completely, but like every good over-generalization it has a nugget of truth: admitting a personal blunder to someone who has no empathy for you is ill-advised. That summer was all about me becoming employable, so I'm pretty sure my uncle meant that I would appear weak to a boss or employer, but the rule holds doubly-true for internet readers.
In the past, I have been tempted to write blogs about my goof-ups. I have almost always decided not to write such posts, not for want of subject material, but because they don't have any upside for me or my company. In the best case, people will think I'm humble, in the worst case they will think I'm incompetent. Simply put, I'm not willing to risk being labeled the latter for the former. And neither should you.
Self-aware people admit failure to get constructive criticism and seek catharsis. You aren't likely to get either if you bare your soul to the anonymous masses on the internet by first saying "I'm sorry."