[Update 04.09.16: The relevance of this discussion can be seen in the discussion around the University of Chicago's explicit non-support of trigger warnings. Good coverage by Samantha Harris at The Fire and Robby Soave at Reason. For a defense of trigger warnings, see Angus Johnston, here and here. Freddie deBoer is always worth reading too.]
Let me try out a simple argument against trigger warnings. It has two simple premises, which taken together lead, I think inescapably, to the conclusion that trigger warnings have no place in education. Not only are trigger warnings bad psychology, they are poor pedagogy.
1. If trigger warnings are not mandatory, they are pointless at best, dangerous at worst. That is, if a teacher cannot be disciplined for failing to warn students of potentially triggering content, then students are effectively not protected against being triggered. Moreover, the use of a trigger warning in one course is essentially a false promise that the student will be protected from uncomfortable reading in other courses. If they are not protected in those other courses, the discomfort may be amplified by a sense of betrayal. If there is any risk of exposure to triggering content, then, this risk must be part of the deal going in, i.e., it is simply what you sign up for when you enroll at a university.
2. Trigger warnings cannot be made mandatory without ruining the educational experience. A simple example should suffice to show this. Ernest Hemingway's "Up In Michigan" is essential reading in a course on early twentieth-century American literature, or literary modernism in general, or the modern short story, or countless other courses. It includes a scene that Gertrude Stein famously called "inaccroachable", as recounted in Hemingway's A Moveable Feast (which is another reason to include it in the syllabus). Anyone who reads this story will, I hope, agree that (a) if any story requires a trigger warning then this one does and (b) if the reader is warned of the triggering content the story is ruined.
It might be argued that universities have no obligation not to ruin a piece of literature, that students should in any case re-read the story, or that a truly great piece of literature can survive a spoiler. But I would argue that a course in American literature should, among the many things it does, expose students to literature they might not otherwise read, and it should then reward the student by giving them the full literary experience of letting a story proceed toward its uncertain and, in this case, ambiguous conclusion.
I'm leaving aside the question of whether anyone would be seriously harmed by reading "Up In Michigan" unprepared. I think very few people would be "re-traumatized" by it, and no one, of course, would be traumatized by it. [But there is a very definite, very important experience to be had by reading it.]* A trigger warning here would rob all the students of that experience. Indeed, a student who opts out on the basis of the trigger warning might also be unfairly robbed since the triggering content may not be severe enough to have actually caused any discomfort, but the careful (and now frightened) student would not know this. For this reason, the demand for trigger warnings should have been summarily rejected by universities from the outset, just as a demand for "easier math" in a physics curriculum should be rejected. Such demands simply misunderstand the nature of higher education. It is natural, namely, that some people will turn out to be unfit for particular courses of study, owing to the "difficulty" (in whatever sense you like) of the material.
*This sentence was missing in the original post.