Goat God said
Then The Goat is The Teacher.If that's okay
Master Crim said
Your character has to have a summoning ability, and I dont think your goat does.
While it is true that summoning is required to be a Demonology teacher, there are other ways to summon with a specific power for it. According to canon, mortals use it in the city often to summon demons. It's not as controlled of a method, but we are in desperate need of a Demonology teacher. Unless Crim just really doesn't want our Goat as a teacher, then he can have the job.
But, as a note to the Goat, try not to get too crazy with it, OK? No constant pranks, breaking doors, etc. Also, you'll have to be able to speak English, unless you want to write everything out to your class (which could be funny)