
firstly- sorry to be blunt, but you’re just wrong bcz the ML suspected our MC as not being the person he said he is (a high schooler) because of when they meet in the library, when the MC destroys the worms the ML sent after him which were specifically sent after someone who could become his successor.
and also, our ML asks the MC how old he is bcz he knows the MC isn’t really the age he’s pretending to be and was just testing him, and MC couldn’t give a clear answer.

Taehee is a very very quick witted person, he realises almost immediately that Jaegyeom isn't a high school boy, most likely right when he discovers who destroyed all the worms because no high school boy is physically capable of doing it.
And as someone who often feels uncomfortable about age gaps (and felt iffy about this too) if it can make it up, in the novel they explicitly say Jaegyeom doesn't know what age he is because he doesn't know when he was born and when his body stopped growing. So he is over 200 years old but his body should be around 18-21, but Jeongju wanted him to go to a school to socialise so he made up his new identity and appropriate age to fit into a high school. Taehee is 26 years old and the school arc and the librarian-student setting is sooo short compared to the long novel that you completely forget it how weirdish it was

Reminder, the story stated that they suspected "someone" who's the gwi thingy would be in the school as a student, but ML have never been able to confirm who it is yet. Hence why im uncomfortable reading a whole ass grown man thinking it's okay to be this physically affectionate to someone he hasn't confirmed to be a high schooler or not yet.

Yes your feelings are totally valid, don't mind what other people say. I also felt weird with the school arc, but Jaegyeom was going to school for only a couple of weeks and then started going to work with Taehee. I think it also helps that Jaegyeom uses korean informal language with him all the time, because he is in fact older than Taehee, but unfortunately because there is no difference in english between formal and informal language to elders people can't pick up that nuance

i get what you’re saying, but he (the ML) has realized who the gwijae is (or he’s at least very highly certain of who it is) and that the MC isn’t just a high schooler. it’s hinted at through, like i said, the worms, the age question, as another commenter said, his form of speech, etc.
it’s valid to be uncomfortable though, was just trying to clear things up for you.
I can't be the only one uncomfortable that ML is openly trying to be physically affectionate with a boy he perceived as a high-schooler? Like yea our mc is basically immortal 1000+ years or whatever but ML doesn't know that. Why is he doing this weird ass shits to a boy he saw as a student??? When he's a librarian of the school??