You are talking about someone with PTSD.
Is that any different than your example with the dog? Or someone who's been raped, assaulted, or experienced some other traumatic event? If so, why is it appropriate to label some potential triggers and not others? Who gets to decide what does and doesn't make the cut? The same goes for safe spaces. You can't use it outside of a specific professional setting without abuse or you get someone who decides that they're "triggered" by Muslims because of their own irrational fears and that their store is now a "safe space" where Muslims are not allowed. Even if someone legitimately believed all of that, it's still a horrible outcome when viewed objectively.
The problem is that the people who want all the trigger warnings are the same people who have no training and want to use them to actively avoid any exposure or to wield them like a club in order to effectively censor those things that they do not like.They want to live in a bubble walled off from the rest of the world and are demanding them everyone else accommodate their demands. If someone has had such a traumatic experience that they can't function in regular society, they need help and probably shouldn't be going to university until they can get to a healthier place. If something makes a person uncomfortable, they should seek the kind of professional help to get them beyond their past experiences. Demanding that anything which gives them discomfort be removed is ripe for abuse and history has shown no shortage of moralist busybodies who do exactly that.
Suggesting that the people at university who are clamoring for trigger warnings or safe spaces are using these appropriately is deluding yourself beyond all credibility. One group of students even published such in a list of demands that they presented to the administration. They directly state a demand for exclusive safe spaces on campus, which would be racially segregated. The idiots making these demands aren't using trigger warnings or safe spaces in the clinical and professional manner in which they might be helpful. Even in the case where individuals want (and it might even be a good idea to have) a private setting to discuss something, that does not entitle them to use public property and demand it be treated as a safe space where dissenting opinion is prohibited. Even less so in an institution where the youth of the world should be having their ideas challenged.