I also want to add to this headcanon (I may be late but...)
So, I agree to the headcanon he was from a poor family, and I use to think it would make sense he had problems with his parents, I doubt he had much friends either. This would be a good reason to scape and become a pirate and this theory also follows the dramatic line of one piece. Maybe he only got love from the cats? 😛
Then yes he became a dangerous pirate and blablabla
When he met Kaya's parents, they gave him everything he never had. A home, love and acceptance, and material goods too. He mentions, at least on the anime, he never planned to kill Kaya's parents, so it wasn't him who did this. This make me think Oda wanted to tell us how Kuro appreciated them, bc otherwise, why telling it? Would be easier to add their deaths to Kuro's plans.
When he's there, though, even if he is treated with the love he never had, he has Kaya there with who he develops a relationship similar to the one of two siblings. That's why he's always jealous of Kaya, because she's always treated as a real daughter, while he's only the butler. Living with her also makes him jealous of all she has: loving parents and their attention, lots of money, a beautiful house and an incredible inheritance.
That's why... Probably he always "hated" her.
Then when her parents die, it is hurtful to both Kaya and Kuro. But he is still jealous AF of Kaya and sees the opportunity of having the life he always wanted when he was a pirate and specially now that he no longer wants to be one; he is tired of being poor and hated, and in the village he was loved, and killing Kaya would make him rich too, that is if his plan works as predicted.
But! After all Kaya is all what is really left of his parents, and he feels the duty to look after her as his butler and his obligation towards the people who saved him some years ago. So he has a love-hate relationship with her. Also, now taking care of her more like a parent than a brother, she starts growing on him even if he doesn't want to admit it. This can be appreciated in the anime/manga scene where he looks at Kaya and puts the blades on her face, like looking at her. It could be interpreted as a cat looking with desire his prey, but it also looks like him thinking if he is doing the correct thing.
But remember, Kuro is clearly a narcissist, so he and his pride go before everything and that's why his plans always go first (even if they are always bad ideas that fail 😂). This is why he goes on with the plan of killing Kaya and doesn't let himself doubt about it. He also has a lot of people involved in it, and obviously, there's no way they can even think he's weak! So he feels like his duty is killing Kaya.
His love towards his parents (and probably towards her too) can also be appreciated in the LA scene where he is in front of the family painting in the room where Kaya hides and he makes his "jealousy speech". He destroys her image in there, but as angry and frustrated as he looks, why doesn't he destroy the whole painting in a rage attack? Instead, he clearly goes for her image and his eyes look wet, as if he was hiding something that hurt him a lot. He was probably making all the "jealousy speech" to encourage himself to kill Kaya, remembering how he "hates her" but even like that, the painting feels to me like doing the opposite effect. This moment is incredibly powerful from my point of view as it seems to talk a lot about Kuro's emotions. It's the first time he looks somehow "small" and really emotional. Also, he later has Kaya right under his blades, why doesn't he kill her immediately instead of just looking at her? Okay Usopp throws him a ball and blablabla, but if he had the urge to kill her, he would just do that in a second while or right before going to push Usopp away. Okay, one could say he is just a cat savoring his prey, and it can also have part of it, but he also looks as he is doubting a bit to me.
Idk this is my theory, I hope you find it interesting and I'd love to read people's headcanones
