I notice that Kagami doesn't say he's a cat the whole time or even act like he's a cat, I was confused but then I read that this was actually the first story and then the doctors story
(and the flexible boy from p.e.? that scene is mirrored in the doctors story, his story was happening at the same time on the same timeline. in his story he gets mad in the infirmary when he goes in and there is the creepy substitute. Also that same black cat is a werecat in the doctors story. If you read his story after you keep seeing Michiru in the background.)
and after that is Kagami's story, then Kagami's brothers story.
They are all interwoven in this big universe.
Every time I saw kagami appear, I screamed a little!