Why, yes, I am picky, and it is neither slasher nor giallo. The vast, vast majority of slasher films feature a solo antagonist, while in Suspiria there’s an entire group. Also, while supernatural elements can be a part of slasher films, it really goes against the whole slasher ethos to use one’s supernatural whimwam to remotely kill your victims. You have to do it personally. (Ironic, considering how in so many slashers neither party has much personality.) Freddy Kreuger entering someone’s dreams counts, because in a certain sense he’s right there with the dreamer. Conjuring up some monster or possessing an animal to do your dirty work isn’t very slasher-esque.
As for being a giallo, Suspiria is an Italian film, shot and/or dubbed in English, that contains a mystery, true, but so much of what makes a giallo a giallo is missing. One major lack is the motivation of the murderers. The killers in giallos kill due to their psychology. Often, although not always, this is a twisted psychology, they’ve been driven mad at some point, but regardless, there is a human motivation. The killers in Suspiria basically do it because they’re evil. No further motivation needed. Also, while giallos sometimes have supernatural elements (and pseudo-science) on the sidelines, rarely does an actual giallo revolve around the supernatural.
