It seems to me that the issue of trigger warnings on websites and message boards largely comes down to a question of politeness. Some sites, commenter groups, and people like them, and therefore using them becomes not only a sign of politeness, but also respect for the discourse community—these are the rules most of us play by, and in order to be a "good" member of the community, you should follow them, too. There's nothing particularly problematic about that—our house, our rules, with some websites using them and some not as a matter of course.
When it comes to teaching, however, that gets a bit thornier. The issue of trigger warnings in classes and on syllabi has been getting a lot of buzz lately amongst the teachers I know, as well as in online discussion—this New York Times piece provides a useful overview of the topic, and over at Salon, Britney Cooper has a good explanation of why she's against them. My thoughts on the matter are pretty equivocal, and if this reads as me trying to work through how I feel about the topic...well, there's probably a good reason for that.
The main objections that I've seen from teachers seem to come down to the following: they're a bad idea for education, because students don't (or shouldn't) need to be protected from ideas. And if a student has a problem with content, they should approach the teacher and deal with it individually—it shouldn't be dealt with on a class-wide (or broader) level.
Taking the objections in order, in principle I agree with the first objection—in many cases, education is about exposing students to new ideas, and so teachers shouldn't hesitate to use texts that will help accomplish that goal (the question of whether or not Text A or Text B will actually be an effective tool in accomplishing that goal, regardless of whether or not the teacher likes it, is another discussion).
Still, I'm not sure that works against the idea of trigger warnings in classes. If I say, "Be forewarned, we're going to talk about ______ in this class," does that minimize the impact of the texts themselves? Does it nullify the ideas the texts contain? I don't think it does—is the element of surprise that pedagogically important?
With that said, even though I'm not convinced by the objection that trigger warnings affect what teachers actually do in class, it is a possibility worth considering; Oberlin College, for instance, made the news after publishing a set of suggestions on its Office of Equity concerns webpage for teacher dealing with potentially triggering material. The suggestions included the following: "Strongly consider developing a policy to make triggering material optional or offering students an alterative assignment using different materials. When possible, help students avoid having to choose between their academic success and their own wellbeing." (The policy has since been taken down, but an archived copy can be found here.) Many teachers—myself included—are concerned by the idea of a university administration telling (or "strongly suggesting") teachers what to do in their classrooms.
I find the second objection more problematic. If we take "triggering" to mean what it originally meant (more on that in a second), then it's…tricky…to say to someone who has been traumatized that it's completely on them to talk to the teacher about the problems they had with the material and why. To borrow an example from a comment I read somewhere, let's take a student in a class reading Lolita who was sexually abused by an adult authority figure in the family. If we are saying that it's on that student to go to a teacher and explain her or his abuse (and it seems like it would have to be their responsibility in this scenario), that seems to be moving into very dangerous waters in terms of what a teacher has a right to demand to know. In addition, what makes me think that I'd be qualified to help a student in that situation? And, if a teacher (with some justification) objects to being told what to do in her or his class, what kinds of accommodation is he or she likely to make when that one student shows up to discuss past traumas?
(For the record, if you're not convinced by that last part, neither am I—while I don't think I have the right to expect students to recount their traumatic experiences to me, I can't think of a way to help them work through their responses to a text if they don't talk to me.)
With that said, there are still pretty good reasons for not automatically supporting calls for trigger warnings in syllabi. The first has to do with mission creep. Look at the evolution of trigger warnings on online discussion boards. What started out as an attempt to keep people from being "triggered" by being faced with traumatic events becomes, in some cases, an attempt to keep people from feeling unpleasant things ("TW: Anxiety"). Trying to avoid re-traumatizing students is one thing, protecting them from things that might make them feel bad is another.
More importantly, trigger warnings shouldn't be necessary. If a teacher provides a course overview on her or his syllabus (as most do), it should provide a pretty good idea of the sorts of things that will be covered in a class. "In this class, we will explore issues of _____." I've seen syllabi that go further and say, "If you're uncomfortable with depictions of ______, you might want to find another class." I'm certain that those statements (which can read a lot like trigger warnings) did little to nothing to affect the pedagogical effectiveness of the class, and they seem like a way of dealing with the issue that is fair to all concerned.
Beyond that, in some cases the very nature of the course should be a trigger warning; Jenny Jarvie of the New Republic mentions a course at Scripps College in which students are given a trigger warning at the beginning of class. The class in question? "Histories of the Present: Violence." I don't think it's unreasonable to assume that a student enrolled in a class with violence in the title should expect to be confronted with texts involving violence.
In the end, both sides need to be aware of the other's concerns. Even if they don't put trigger warnings in their syllabi, teachers shouldn't dismiss the request from students out of hand. It's not just about students wanting to get out of being challenged, any more than teaching is just about being shocking and in-your-face because good teachers are edgy. Both views (which I've seen expressed in more than a couple of places, and in different contexts) are needlessly reductive.
For their part, students need to realize that even if they've become accustomed to trigger warnings on a message board, the warnings are there for a reason: the community of like-minded individuals have entered into a tacit agreement to warn each other out of politeness. It's a way of all being on the same page. That isn't what a classroom is about; it's about learning things, being confronted with challenging and, at times, triggering texts.