I'm really sure Cavendish wants attention and love because he didn't get them when he was little. My main fundaments are:
1) He got kicked out his kingdom for Hakuba. At first, it seems normal. He killed people, right? But then, you start to think about it.
The DID (Dissociative Identity Disorder) is developed as a survival mechanism to cope with severe, repeated trauma during early childhood. Maybe Hakuba was a way of defending himself from something. For sure, he wasn't having an amazing time back home.
Bartolomeo figured how to contain Hakuba in LESS THAN ONE DAY, tying up Cav. But his parents solution was just... kick him out? That doesn't scream parental love to me.
2) Oda usually makes characters want something they didn't had in their childhood. Whitebeard didn't had a family, so he started yearning one. Usopp didn't have anyone that cared for him for some time, so he started yearning attention. Nami didn't had money of her own bc she was saving it for paying Arlong, so she wants money for herself.
So it makes sense that Cavendish wasn't loved in his kingdom. Sure, maybe his beauty was admired, maybe girls found him pretty, but he wasn't truly loved. Maybe he learnt to take that admiration as love. When someone "steals" his spotlight, he gets mad because they're stealing his chance to get love.
3) How much he loves his horse Farul. This might be just my weird brain, but hear me out. Animals love you for how you treat them. Not for your looks, neither your reputation. Besides, he had him since he was a little kid. He probably was his only friend, the only being that loved him no matter what.
Sorry this got so long hehe, but this has been on my head for a while