My argument is that whether the idea of a "safe space" is warranted, and who should be allowed to make use of such a space, are different questions.
A "safe space" might have valid medical reasons to exist—in fact, it would likely be a concept quite easily unified with that of a counselling office.
But, for it to have the correct incentive structure, it would probably require you to get a note from a real honest-to-god psychiatrist at the beginning of the year before you could make use of it. Otherwise you end up in the stupid rut of the "ignorant-but-unaware-of-it" people avoiding the very properties of an education designed to bash their narrow views open.
Perhaps don't attend that speech then? Life at a university doesn't involve dodging "pro rape" speeches blasted over the PA system multiple times a day.
The recent article about the "safe spaces" full of coloring books and toys notes that people were fleeing to those rooms simply because _someone was on campus giving a speech that challenged their beliefs / "triggered" them_. If universities are catering to folks that simply can't handle the thought of someone with a conflicting viewpoint talking on campus then the ideals of the university truly are dead.