Does japanese people believe (as an old tradition or something) that rabbits came from the moon? It's that so, isn't interesting that Rukia have this strange taste for rabbits and she's the "moon"?
Yes! East Asian folklore often links rabbits to the moon, based on pareidolia that makes out the markings on the moon to be in the shape of a rabbit.
I’m not sure about the Korean or Chinese versions of the story–which I think involve a moon goddess, whose name escapes me atm–but I think the Japanese version has the rabbit pounding mochi?
There’s a more blatant reference to this in the Sailor Moon series, where Sailor Moon’s real name is Usagi Tsukino– Usagi of the moon— and usagi, I’m sure, means bunny rabbit in Japanese. Good pick up, Anon!