Princess Kira and mistress Sofi wanted their boyfriends to stop taking things for granted and they turned them into their human ponies. They had the boyfriends carry them on their shoulders and even urged them to race promising rewards for the one who won. The guys were humiliated but they learned their lesson and they did what their girlfriends wanted them to do so as to avoid such humiliation again.
Lady Scarlet had always admired horses but she did not like the expenses involved in owning them. She realized that since she had a slave, she technically had a human pony and after that, she never looked back on having her slave carry her around whenever she felt like. It was a lot of fun for her but it was a nightmare and torture for the slave who had to physically carry her and endure whipping.
Princess Diavolo used her whip to enforce the discipline of her slave because she could tell that it was waning. She did not want him to become the sort of slave who did not heed her calls and who did not follow her instructions. They were not equals and she did not want him to behave as such. So she got on his back and she rode him as a human pony while whipping him.
When this guy tried to steal mistress Zora's sensitive documents and then blackmail her for them, she caught him just before he pulled off his scam. He wanted to play the age card on her as he had done so many times but she did not care about his age. Just what he did. So she punished him by riding his back like a pony and she did it for hours and broke his back doing it.
Mistress Amy wanted to ride this loser because she was bored. She did not pretend that he had messed up or there was any other reason why she was doing it. She chose to do it specifically because she felt like it and she was bored. So she put a saddle on him and she rode him as she wanted. She did not care how he felt and nearly broke his back doing it.