I bet he can see spirits too, based on a comment he made to Miko. Whether or not he's torturing the pets, he's being tortured by the ghost of his mother. Look at his eyes. He can't remember his students' names. He seems really out of it.
As to his flashback, my guess is that he took out his frustration from being abused on pets. At least one time. Or maybe he was comforted by petting stray animals, or tried to keep a pet, and his mother forced him to kill it. Actually, that's extremely likely. She looks like the kind of woman who would make her young son kill a kitten. This is bumming me out.
For all we know, the animal spirits could be following the mother instead of Mr. Zen, but because his mother's living in him, it looks like they're there for him.