She kills the praying mantis, she kills killers, bad things. She does love her brother which is why I think she'll kill Oh Inseop (he is the praying mantis). Oh inseop kills indiscriminately to get the object that shines, he even killed his own sister for a pen. She will kill to protect her brother. Her cousin was lucky the cops saved him from her (he did deserve to be beaten to death tho). I think once she kills Oh Inseop she'll find murdering those like him justifiable. All this is show in their childhood interactions with insects. I strongly believe it's foreshadowing.
I don't think she ever will find it justified, does not seem to align with her personality. Until now she never managed to even cut inseop. She is a normal person psych wise, she has empathy and love, she doesn't suffer from the same mental issue inseop does. Inseop totally lacks empathy on a pathological level that you cannot achieve if you are not born with that mental condition. That she will probably kill him we all know, but to turn into a psycho like him is unlikely cause you need to be born like that.

Okay this is such a stretch but in an alternative timeline I lowk want her to break and become more psycho than inseop but is better at masking / hiding it and even hiding it from the detective and the final chapter is her seeing someone as an insect like inseop does (like if she remains a teacher she sees her boss as an insect) then it ends but like she’s kinda learnt everything from him