The thing is in chapter 0 or 1, you see that the person that guwon killed is not his dad but someone who was trying to rob and kill jinwoo. The flashback of guwon killing jinwoo’s dad seems more like his imagination. Because in past chapters, jinwoo has had flashbacks of his dad holding up what appears to be wood while jinwoo’s on the floor. Even before he knew of guwon’s nature, his head would hurt whenever he would try to think of the memories he lost. Like when his dad‘s mentioned, he gets a bad headache and it’s implied that it’s because something bad happened before guwon got there. There’s been a ton of foreshadowing that things aren’t what they seem. Also, guwon knows how jinwoo’s dad looks like bc he picked up the family photo that’s why he said “no I didn’t kill you dad”. He also doesn’t seem like the type to lie. Also when they met at his place and guwon goes “surprise, he never says that he killed jinwoo’s dad but that he’s trying to help jinwoo regain his memories, even if they are very sad”.

I have the impression that the MC killed his own father, but I also have the impression that the author will come up with an even better plot.