I reckon it's the last part of your speculation. Just because of the way Guwon mentions to teach (when he was about to cut off his own goddamn finger) that he knew something was wrong so didn't REM sleep (iirc).
And the amount of times Teach tends to black out before something gory/someone dead gives way to the idea that Teach is probably extremely fucked in the head just as much as Guwon or potentially worse.
Teach probably doesn't even realise that part of him, so his perception of everything is twisted or more fit with the 'morally' correct vision. Honestly, it makes Teach such a fascinating character; his unreliable narration makes you think on what the hell is happening.
Maybe Teach is going so far with helping the doc and such is because he is suppressing something deep inside that he cannot accept. He absolutely cannot accept this world for what it is and what it has taken away from him. He also cannot accept the fact that he has the feels for THE guwon aka the ultimate glowing neon light that says “hey so everything is fucked up”
Hes clinging to what little humanity he has left in a world where clearly morals are thrown out the window because survival has been put over morals. and in a world where survival trumps all, Guwon who is obv the strongest will thrive and people will cling to. Teach sees this world as inhumane and Guwon is the ultimate reminder of that.
Which is why he is trying to take any and all steps to try to oppose anything surrounding him. Obv we know as the audience that teach has some feels for guwon (its bl afterall) and so hes trying to surpress all that. Im pretty sure Teach is gonna give in tho but we will see
just blabbling tho

Whilst I agree Guwon is a monster for his obvious superiority complex and lack of humanity beyond the now one other person he’s decided is his equal.
I do find it odd that Teach is going so far for the doctor and the black hair girl from still water. I think Guwon’s atrocities against mankind is justifiable enough.
Teach hasn’t known nor spent any real amount quality time with any people other than Guwon and the kids. So him caring the Doc’s ring seems very odd to me. I’m not saying he would be sadden, shocked, and moved by his murder but he’s speaking as if it’s one of the primary catalyst for him planning to killling Guwon which doesn’t seem justified.
I think he should spend less time trying to find sense in this broken world and use his obviously considerable influence over Guwon. To shift his world view for the better np because killing him is highly unlikely considering he just single handedly wiped out an entire group of survivors with just a baseball bat.
Right now Guwon in all of his murdering and entrapments is convinced he’s a hero and amazing and good….imagine what he’d be like if you tarnish that….upend his little kingdom? He’d be a walking catastrophe I think the one path forward is teaching him a better way.
But idk if Teach can even do that considering he likely has some kind of personality disorder. Something tells me he’s actually just as murderous as Guwon but has compartmentalized that part of himself as some sort of defense mechanism.