The teacher is not a reliable narrator, in my most humble opinion.
Personally, I believe that HE was the one who killed his father, NOT Guwon. He's just looking for someone to blame because he's feeling guilty.
From the few flashbacks we saw about his memories, it didn't look like he had a great relationship with his father/family.
Maybe I'm wrong!! If I'm actually wrong, then MC choking Guwon might be explained by the fact that (allegedly ) Guwon killed MC's father, and MC's subconscious remembers that and is trying to get revenge.
I could not care less about the second couple rn If they were side stories at the end, then sure. But having the second couple share the spotlight with the main couple is kind of zZzzZ