Yoon Jay have mental problem from when he
got separated from his mother when he was a child. He can't cry at all and I think he have difficulty with emotion like normal people.
I recommend to read the novel
Possible novel spoilers:
Yup, Jay is a sociopath (or maybe psychopath). His mom always wanted him to feel something and would always show him dad stuff hoping to elicit some kind of reaction but Jay was unmoved. The reason why he was so attracted to Yoohan was because the first time they slept together was the first and only time Jay felt “sadness” and he was curious about that unknown feeling. As for why he’s demanding sexual from an injured Yoohan? That’s Jay through and through. He’s mad that Yoohan got himself injured and he’s always used sex as a means to get Yoohan to feel anything so it’s not really out of character for him.
He wouldn't even wait 6 weeks to fuck his wife post partum. The man got stabbed and showed you a place that's emotionally important to him, and you can only think with your dick? Goddammit, at least show some character depth-