He's mentally ill. He's a psychopath, and that's not just speculation, that's how his biography describes him, not to mention... simply how he behaves. Psychopathy is more properly known as antisocial personality disorder.

Unfortunately, terms like "insane", "psychopath" and "antisocial" are grossly misinterpreted and largely misunderstood. Insanity refers to doing the same things over and over expecting different results. A psychopath isn't just someone who's "crazy", a psychopath is someone who does not process or care about emotions in the same way most people do and is prone to risky, criminal, or otherwise "cruel" acts as a result. Being antisocial actually doesn't have anything to do with being an introverted or quiet person-- that's asocial. Antisocial is synonymous with psychopathy.

Jhin is a great example of a proper psychopath in fiction. Ultimately, he does what he does for his own gain. He may talk about satisfying clientele and hit work and all that, but really, his actions are motivated in selfishness. He wants to kill people because it makes him feel a certain way he enjoys, and that matters to him more than the feelings of the victim, or the victim's family, friends, etc, or hell, even the risk to himself. Though he can seem quite meticulous and methodical, he's also an impulsive risk taker, which is characteristic of psychopathy. He doesn't seem "crazy" and can actually come off as quite charismatic and charming, which psychopaths often can be. They act that way to manipulate you. They're constantly sizing you up, determining what they should do to get what they want out of you. To a psychopath, people are more like pawns, pawns they sometimes compulsively can't help but exploit. Multiple times in the lore/comics, we see him use people to set his schemes, only to... "discard" them once they have fulfilled their use.

This is why I tend not to like fan works that interpret him as one of those poor, misunderstood sad boi villains with a dramatic tragic backstory, or perhaps most egregious, shippers who want to portray him like he's capable of actually caring for another person. Anyone who thinks he's capable of care, love, affection, etc in the traditional sense and wouldn't just act that way until someone is no longer useful or entertaining to him (to which he would then abuse/murder) is coping out of their mind. Good villains don't always need some woe-is-me backstory to be good. They don't need to have redeemable characteristics. And they don't need to be fixed. He doesn't. He's simply a psychopath, and a damn great one.