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According to Tohno Stories, men are dismembered by tengu and women are abducted by mountain men while children fear youkai monkeys called futtachi.
In contrast, a kappa mischievously attempts to drag a horse into the river, only to be dragged out to the land and all the way to the stable and is captured by humans. The kappa eventually leaves the village to live in a pond at the promise that it will no longer play mischiefs.
The tale that a kappa drags a horse into the waters is called 「A kappa hanging to a horse」. In fact, this tale of a kappa's failure seems to be very general, not limited to Tohno Stories.
As for the doubt of why the kappa tried to drag the horse into the waters in the first place, there is the hypothesis that this originated from that horses and cows were offerings to water gods. Considering kappas are said to be what water gods become when they fall(零落), this is reasonable.
Speaking of which, I found an interesting interpretation about the story of a kappa hanging to a horse. It's the article 「Tohno Stories 58: Thoughts about the kappa hanging to a horse」 in the website 『Let's web Tohno stories!』 (http://iwatenogo.exblog.jp/)
What if Nitori was an abandoned human turned youkai? Upon thinking that, I couldn't stay still without making it into a comic.
Perhaps I'm feeling what the adults who came up with the kappa story felt, wishing for someone to drag me out.
Why must humans be so arrogant?
"The fallen god shed her unholiness following our guides and returned to be a true god."
This is what a villager in 『The Fall』 says.
Many kappas reside in ponds. But ponds are where flows stop. It is impossible that a child would be purified upon reaching it.
Hence I suppose that the wish of a kappa, in other words a child, to be purified raised the kappa from the pond. That is, I'm suggesting the story is not about how the kappa tried to drag a horse into the pond but how the horse rescued the kappa out of it.