Small animals in Japanese are counted with 匹 hiki. Large animals are counted with 頭 tou. Rabbits are counted as if they were birds, because logic.
Back in the olden days, all animals were 匹. When doing my pre-writing double-check-googling just now, I found one source that suggests this kanji gets its shape from a horse butt. Oh that makes sense, you much too optimistically think, I bet that’s because it’s used for counting horses, right? Weeeell… it used to be, but then English came along and ruined everything with its fancy phrases worth stealing.
I couldn’t find any confirmation for the following, but my more literate friend told me this a while back:
Natsume Souseki, also known as that guy with the mustache who used to be on 1000 yen bills until he was dethroned by that guy with the floofy hair, is the person who popularised 頭 as a counter for large animals. I did find confirmation that it was popularised in the Meiji era, and of its English origins. When counting cows, they’re counted with heads of cattle.
My farming lingo isn’t up to scratch so I’ll take google’s word for it. Our boy Natsume Souseki decided this sounded really neat, and decided to count that way in one of his novels; 頭 is read as tou when used as a counter, but it can also be read atama, which means “head”. Ever since, tou has been used for large animals, and hiki for small ones.
Small animals, except for rabbits, that is. Rabbits are a special case, and are counted with 羽 wa. My dictionary tells me that when read hane, this means “feather” or “wing”. Wa happens to be the counter for birds, so the feathers and wings make sense. There aren’t any definitive answers as to why rabbits are counted as birds, but there are a couple prevalent theories. The first is that the Japanese words for “to fly” and “to jump” are pronounced the same (tobu, I believe the kanji are 飛ぶ for to fly and 跳ぶ for to jump, although I might be mistaken and they’re both 飛ぶ). This theory is generally countered with “frogs tho, they jump but are counted with 匹”. The second theory suggests that once upon a time, there were a group of monks. They weren’t allowed to eat animals, only bird meat. But, they really wanted to get in on some rabbit meat action, so they declared that rabbits are totally a kind of bird.