Part of the issue is the misuse of "trigger." A "trigger" is correctly something which causes or risks a mental health crisis in the person exposed to it.
Most often this happens to individuals with post-traumatic stress disorder. Triggers can be very mild (in which case controlled exposure can make them go away. For a while, thanks to the pandemic, I was mildly triggered by the smell of lavender. I got over it and was able to convince myself not to be silly) or they can incapacitate the person.
People misuse trigger as "thing which makes me uncomfortable."
That said, content warnings, which are not the same thing, are a good thing. For example, I have issues with body horror that involves eyes or teeth. If there's something like that in a movie or TV show, I handle it much better if somebody warns me it's there. And people are not good enough at all about warning about strobe effects in visual media, which can cause *physical* symptoms in certain people. I put content warnings on certain of my books that have higher levels of interpersonal violence. It's not unreasonable to ask a professor to give people a head's up when, for example, sexual assault is going to be discussed, because it is very likely somebody in that class *has been raped*.
It's a balance. You're absolutely right that this can be weaponized but sometimes one wants a warning ahead of time that something that might be personally difficult is going to be discussed. I don't necessarily think students should be allowed to skip that class, but most people can deal with stuff that makes them uncomfortable with warning.
And I'm a queer person and know all about being weaponized.
I use the term "content warning" rather than "trigger warning" because it doesn't imply the content being warned is bad, gratuitous, unnecessary or harmful. Just hey "This episode of Doctor Who has giant spiders crawling on people's backs to take over their minds" is something an arachnophobe might want to know. (And yes, there actually is an episode of Doctor Who in which that happens).
(And, of course, there's a difference between warning people about entertainment and teaching accurate history warts and all).