Yep you nailed it. And remember we never saw his mother's face too in the picture. Maybe MC's dad did something to the mom idk and then MC had to defend them
See, THIS makes sense given what we know about Guwon and his method of sparing people.
It'd make sense for him to kill someone who is a thief in his eyes. He doesn't need someone he can't trust to not raid their supplies since they are so precious.
It'd also explain how Jinwoo is just laid out and already injured when Guwon finds him. Some people seem to think Guwon spared Jinwoo 'cause he was interested/in love with Jinwoo at first sight, but that would make 0 sense given that Guwon can't even grasp basic emotions and the only brain cell he's got is focused on weeding out the weak and bringing the strong back home.
He wouldn't keep a person who is clearly injured and "unable to defend himself" ((for now 'cause I'm holding out hope Jinwoo is secretly a bamf)) alive let alone bring them back if he couldn't confirm they were useful.
I think the teach killed his own father. He has vague memories of his father raising his hands up as if to strike him with something. That’s probably what made him weak when someone came in looting and Guwon killed that looter before he can do anything to teacher.