When people ask, answer, or comment, why must they keep using "Emphasis mine"? The section is bolded or otherwise emphasized so I feel that the statement is completely wasted. Am I missing some reason why it is used so often?
We say "emphasis mine" alongside a quoted passage to indicate that emphasis inside the passage is not in the original, but was in fact added by us. It's shorthand for "I added the emphasis here myself".
We do this because emphasis in different places can change the meaning of writing, so it's important to note that any meaning read into the choice of emphasis is just part of us trying to highlight something, not some meaning that should be read into the original writing's meaning.
It's a common English writing convention. “Emphasis mine” means that the emphasis was added by the person using the quotation. This is as opposed to “emphasis original”, which is used to indicate that the emphasis is part of the original quote, not added by the later quote-user.
Like bracketing changes, inserting ellipses, and using sic, indicating who is responsible for the emphasis in a quotation is a way of preserving the integrity of the original quote and establishing the bounds of the accuracy of the quote.