If Gaeul really is bullied, the author did quite a lame job showing it, it looked more like her classmates criticized her, and it's true that people talking in weird ways like some chunibyou is annoying. I mean, if you want to portray a bulling victim, don't fucking draw them quite, jeez.
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The fuck are all these 2nd years doing on the 1st years floor all of a sudden, lol.
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Imagine a chad fucking coming up to you the-pathetic-virgin and telling you to call 'em up bitches.
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"You got 500 won?"
*instantly gives him the coin*
Man, I haven't slapped my forehead so hard for months XD
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Gaeul has a black belt in Karate or something similar (it shouldn't be Taekwondo, otherwise she'd reveal it). That's why she's so chill about all these fighting and her classmates.
An obligatory note about black belts being divided into ~10 ranks in most martial arts, and that Shodan and alike basically mean the first level when you can call yourself a proper practitioner rather than a master. Also it can be explained as people getting a black belt merely means that they are serious about their art. I always saw it as 'people that may leave anyday' (colored belts) vs 'people that are actually doing the thing.'