After I read your comment I went back to reread the earlier chapters and I think you might actually be on to something because Guwon even said he just woke up and “everything was already decided” for him. Maybe they are going through a loop situation and that’s why he thinks Teach is more special than everyone else? Plus he said Teach already tried to kill him multiple times but our Teach hasnt really done shit hes only started his honeypot mission lol
I think I get you, if let's says the hounds of Sisyphus might mean that Teach really wants to kill Guwon but as we read here he can't help but still have feelings for him, so there might be a chance that teach might go a 180 when the rebellion happens and turned against them in favor of Guwon and then went he rebellion lost, it'll be all over again as they try to find more people to replace those that got punished from the rebellion, and then teach will hate himself again and will want to kill Guwon but as the title points out he won't be able to kill Guwon. That's or Guwon is someone who can't physically die, as he is very weird with his personality and how he dismisses dying, he'll always come back to life and teach will always to to kill him but he won't be killed and the rebellion will just be for naught, sooo this also can apply with the title meaning, as teach will always try to kill Guwon and Guwon can't/won't just be killed or stayed dead ╮( ̄▽ ̄)╭ (〜 ̄△ ̄)〜

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I looked up the meaning of Sisyphus, and the term Sisyphean refers to a task that is impossible or seemingly impossible to complete. It comes from the Greek myth of Sisyphus, who was condemned to push a massive boulder up a hill for eternity, only for it to roll back down every time.
So, that made me think that Teach's struggle is actually Sisyphean. Correct me if I'm wrong, but don't they live on a hill because of the spreading infection or apocalypse in their world?
I started connecting the dots because I have a feeling Teach will eventually lead a rebellion and try to escape Guwon's control. If that's the case, then his rebellion itself could be a "Sisyphean" task...something he's destined to repeat without ever truly succeeding. That would explain why Guwon was so confident when he said he would let Teach kill him if Teach ever chose to rebel. Hmmm...
Symbolically, Teach is Sisyphus, endlessly burdened by his fate that he cannot escape (like Sisyphus carrying a boulder on his shoulder up a hill eternally), while Guwon represents the boulder here. He is the weight Teach condemned to carry for eternity. No matter how hard Teach struggles or how many times he fights back, he always ends up right where he started: bound to Guwon, whether he wants to be or not. That's why it's called The Hounds of Sisyphus. For short; Teach's cage. This is an another Doomed BL in the History.