I was reading a reddit post on a scene from Star Trek: TNG. One of the responses was of particular interest:
... apologizing to a subordinate officer in front of other staff would mean failing to maintain decorum on the bridge and a huge failing in a Captain. Asking him if he's ready to return to duty is recognized as an apology not only by Wesley but to everyone who witnesses it, because they're all aware of the protocol.
The answer is summed up as this being the correct action because of protocol.
What is meant by an apology in this context inappropriate? Is it merely suggesting that an apology should be made it private and not on the bridge or in front of other staff? I'm particularly interested in a better explanation of it being a failure to "maintain decorum".
I understand that the example is fiction but my question is with regard to the comment and how a situation like this might occur in the workplace; for a better understanding on how to act within a management position. I would also welcome comments on additional real-world examples of similar situations for clarity.