Seeing as I have nothing better to do, I’ll be writing down my speculation on the contents of this chapter here, so don’t read this until you’ve read the chapter first.
Still here? Well, alright.
Essentially, I think Teacher was made from one of Fenrir’s Fangs.
My reasoning is pretty simple. The fact that the wolves are Kin makes it obvious that Teacher’s related to Fenrir, who I’m speculating as either sealed by the Gods — perhaps for reasons similar to Fenrir’s sealing in Norse Mythology — or transcended and became a God, with the latter speculation being what I’m leaning towards given the mention of the God Wolf in Urushi’s Titles.
Anyways. Teacher being able to summon wolf-kin would only make sense if his body was exceedingly similar to that of a wolf, so I’m about 80% sure he’s made with Fenrir bits. The other 20% is due to the possibility that he was just a sword jabbed into an altar to absorb Fenrir’s essence like a magnet, thus eventually becoming so attuned to Wolves that he can summon them. In that 20% case, I’d go with the ‘sealed’ story for Fenrir. For the 80%, I’d go with the ‘transcended’ story for Fenrir.
Or maybe it’s something entirely different. *shrug*