When is a red herring not a red herring.

Consider for a moment a simple example of a red herring: A teacher catches a student cheating during a test. The student in response says, “I know I’ve made a mistake. But think of my parents. They’re going to kill me”. In most circumstances this would be considered a red herrings.

Suppose that the student was Charles Manson Jr whose proud parents were Charles Manson and Lizzie Borden. [please accept the obvious logistical problems with the parenting]
Would this still be a red herring?

I'm gonna say the first example might not actually be a red herring because the phrase "going to kill me"might be metaphorical so it isn't literal and the second example could be considered literal. Your reasoning in regards to this might actually be a fallacy of equivocation because your argument changes the meaning of kill in the second example. I do tend to read more into trains of thought than I should at times...I'm sure I'm not right.....

I would lean special pleading.

I my latest version of the book, I have refined the criteria for logical fallacies (according to me). They are:

1) It must be an error in reasoning not a factual error.
2) It must be commonly applied to an argument either in the form of the argument or in the interpretation of the argument.
3) It must be deceptive in that it often fools the average adult.

In your example of the teacher and the cheating student, we would need to read between the lines to see if there is an argument involved. For example, it could be that the kid is just giving a reason for cheating (bad if he really will not be hurt by his parents, good if he would). There would be no logical fallacy here. However, if the argument went like this:

P1. Cheating is allowed if the student's life is in danger.
P2. The student's life was in danger.
C. Therefore, cheating is allowed.

1) One could argue with premise 1. But still no fallacy.
2) One could argue with premise 2. But still no fallacy (the student could be just lying).
3) If P1 and P2 are accepted, the conclusion follows.

Perhaps the argument COULD be rephrased in more fallacious ways, but this would have to be spelled out. I don't see an obvious red herring here so I can't say that having a legitimate threat would negate the red herring. The reason I don't think a red herring is involved is because the fact that the student feels threatened by his or her parents is a valid reason for cheating. Parents do push too hard at times. Now, if the student said "It's okay that I cheated because Billy gave me the answers. If you want to stop a cheater, let's look at Billy!" That would be a red herring.

I'm more used to hearing about a "red herring" in literature, specifically, mystery stories. There, it is a point that has absolutely no bearing on the main mystery, and is presented as a deliberate attempt to distract people from the real issues. Truthfulness or falsehood does not affect whether something is a red herring.

I suspect the same is true with your examples. Both cases would be red herrings, in that the fate of the student at the hands of his parents, probable or not, does not affect the fact that in both examples, the statement "my parents will kill me" is a red herring.