Responses
I could agree to this. We get a view of Jinwoo's dad in one of the earlier chapters, and even though they seemed to be friendly, there's a moment where the dad seemingly loses it and hits Jinwoo. Although, Jinwoo also has gauze on his head, and unless there were first aid in that kit, there had to had been some time between his father's outrage and the moment society crashed.
What if Jinwoo killed his own father and that’s why Guwon says it with certainty? Or, maybe, Jinwoo’s dad had attempted to kill him and ran off. That would explain why when Guwon stumbled across him, he had already sustained a head injury. Just throwing ideas out there.