We had been working unwise hours for several days, and we got the fix together, and I made a mistake: I pushed it directly to production.
Man, my boss was really mad; no one had been getting enough sleep and we were all stressed. I apologized profusely and said it would never happen again. Fortunately, the fix was correct, so this could have been worse.
Ok. Do you notice what's missing from this story?
We never addressed the flaw in our deployment which made it possible to push to prod without passing test.
Apologies are for when you harm others. Some mistakes do, and some don't. A blanket policy that a mistake is an occasion for apology and navel-gazing is culturally harmful, because it casts mistakes as personal failings, when they are frequently the result of institutional or procedural shortcomings which can and should be addressed.