He didn't have to reason with him. He just had to not fuck him. Did he wait for Dan to see reason before taking him to the hospital? No? Same thing. There is no point to trying to "understand" this character, truly, because he isn't really one, as written. It's just rape logic drawn in human form.
dan wanted to "pay jaekyung back" for taking him to the doctor and booking a room for them, that's what I meant. he does feel like it's another debt to pay off, and jaekyung is still too big of a bitch to tell him "no, I'm doing it bc I worry about you". instead, he ends up playing along, like he doesn't care about dan. and maybe he genuinely believes he doesn't, idk. there's not much to work with bc his personality is almost non-existent. he shouldn't have laid his hands on dan, he should have said no – I would appreciate that, a small win in favor of jaekyung getting some character development. but it is what it is.
not to defend jaekyung, but I think he only agreed to have sex right now bc it was no use trying to reason with kim dan (+ he probably got hard bc he's a beast; but having sex was not on his mind initially and it shows). not that it's okay, but what is in this story?
I just hope he will start to truly care about danny as a person, not just a fuckbuddy. and I need jaekyung to prioritize dan over his own needs at least once. then I will start to believe he can get redeemed.