He's not human, like his backstory says he's a snake (or a serpent to be precise), it's a being that originally doesn't meant to have these humane feelings, but after years of being a human to stay with Leila, Edwin start to become more and more attune with his humanity
And that includes twisted feelings ones have when they are in love / like someone too much. Take it this way, sometime a person would have cuteness aggression when they see something so cute right? But we never actually meant to act on those action cuz we knew better! Yet the feeling is there anyway, and that feeling is what Edwin felt for Leila times x1000 due to his serpent nature. "it is a dirty being" as the narrator says in one of the chapter.
He wants everything Leila felt or think BECAUSE of him, so it mean that Leila will alway think of him as much as he thinks of Leila. This ofc include wanting to see Leila cry or harm him, the emotions he felt for Leila was so strong and overwhelm for him that it clouded the rationals and mix instinct with desire.
He wants all of Leila to be his, including the ugly and unfavorable, the adorable and loveable. That's why Leila says, "this is why he's sometimes warm but sometimes cold", cuz Edwin was soo overwhelmed in his yearning and love for Leila mixing with his serpent instinct, he doesn't know how to regulate his emotions and thoughts properly.
In a way it's romantic, because Leila recognised these and still choose to reciprocate Edwin feelings back to him, because as much as we only seen Edwin insane side, it's evident from Leila flashbacks that Edwin had always been there for him too, and Leila love every part of him back.

Wait i’m dumb and kinda confused but why do Edwin have certain thoughts like wanting to see Leila struggle or cry? Is that his inner snake talking or what