Suppose one person in an argument claims that the other has committed a fallacy. Whether or not the accusation is true, the accused is now distracted from the original argument and has to defend against this new charge. That looks like the accused has thrown a red herring into the argument.
Could the very act of calling someone out on any fallacy be itself a fallacy, in particular, a red herring?
In general I don't want to claim that all mention of fallacy is inappropriate (that it, itself fallacious). For example, I expect two lawyers in a courtroom should be expected to point out any fallacies to the judge and jury committed by witnesses or opposing lawyers. That is part of their job.
However, accusing another person of a fallacy can be damaging to the accused. Not only is the accuser saying that the other person is wrong in the current argument, but they are suggesting that the other person is irrational. There is no reason to trust anything an irrational person has to say.
Given that perspective, there is an underlying ethical issue involved as well.
I am looking for references that clarify whether pointing out a fallacy is itself a red herring fallacy.