Just because your family is abusive and shitty doesn’t mean you want them dead. Abuse creates complex mentalities. Cheol is a victim who never got the chance to sever his own ties. Even for victims of abusive partners, it takes an average of 7 attempts to successfully leave them, and this is his family who he was raised with. It’s not simple or easy.
Also Minyoung is pretty much all Cheol has, and if he kills his family he will go to jail, so they won’t be able to be together anymore. Also he just woke up from a severe injury/head trauma so of course he’s confused and disoriented.
The mental journey of an abuse victim/survivor is not black and white.

Minyoung could throw acid or whatever I'll support him but THAT CHEOL IS ON MY NERVES??? WHAT DO YOU MEAN YOU LITTLE SHIT IS WORRIED ABOUT YOUR FUCKASS FAMILY ?