Two Korean words that make the concept click:
체포하겠어 = 체포 (arrest) + 하다 (do) + -겠- (I'm going to), so it's not "arrest!" but a firm cop-style "I'm going to arrest you", used here as a confession.
The case board in teaser 1 said 어장관리남, literally "fish-farm manager guy": slang for someone who's sweet to everyone and keeps people on the hook. That's why the line 말했지 습관성 친절은 범죄야 ("I told you, habitual kindness is a crime") is the actual charge.
I wrote up the key lines word by word, free and no sign-up, if anyone wants it:
https://www.theidol.ai/en/songs/ill..._medium=community&utm_campaign=rel-illit-fans
(I'm on the theIDOL team; AI-assisted, checked line by line.)