My theory is his dad steals from guwon car or something. You know how guwon feels about stealing.
Or him killing his own father is kinda believable too cause he's known to take knife and try to unalive himself. Maybe he's on one of his episodes and accidentally killed his dad when his dad tried to prevent him from killing himself.
Maybe guwon witness the scene too from afar maybe

I still think that the teach killed his own dad