An example, by way of “The Root of All Evil” by Richard Dawkins:
Science is about testing, comparing and corroborating this mass of evidence, and using it to update old theories of how things work. I do remember one formative influence in my undergraduate life. There was an elderly professor in my department who had been passionately keen on a particular theory for a number of years. And one day an American visiting researcher came, and he completely and utterly disproved our old man’s hypothesis. The old man strode to the front, shook his hand and said, “My dear fellow, I wish to thank you. I have been wrong these 15 years.” And we all clapped our hands raw. That was the scientific ideal of somebody who had a lot invested, a lifetime almost invested in a theory, and he was rejoicing that he had been shown wrong, and scientific truth had been advanced.
An example, by way of “The Root of All Evil” by Richard Dawkins:
This anecdote literally drives me to tears.
What does this have to do with apologizing?
Both involve admitting that you’ve been wrong?
That is a thing they have in common, but that seems insufficiently specific to justify the relevance of that anecdote to this post.
Especially since I don’t recall the linked video saying much about making sure you’re wrong before apologizing.