okayyyy,,,, Heavy spoilers for the novel
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Ms yeon and all the teachers apart from Gajin's homeroom teacher are part of the cult. They want to have access to the other world beyond the gates and in order to do that they want the prophenized child, who must awaken tto their true power. There's been some clues about it, like Sunwoo's awakening coming from the repeated retraumatization and that being analogous to Gajin's loops...also Ms Yeon is the head of the cult i think, due to her ability allowing her to explore the other world kinda (don't quite remember but it's something like that.)

I just cannot contain my hate for Ms Yeon I can't wait to see Gajin beat her ass ヽ(`Д´)ノ