If you meet a talking cat there's a good chance you are a witch or the cat is a witch or maybe both of you are witches
Moth discovers she's a witch for the first time when she's thirteen and being bullied at school. To be more precise, Moth performs magic for the first time when she's being bullied at school. She doesn't find out she's a witch until later when she's talking with her mom about what happened. Moth's mom does not practice magic and forbids Moth from doing the same. This just makes the 13-year-old want to know more immediately. Coincidentally, at this same time, Moth meets a cat who happens to be possessed by the spirit of Mr. Lazlo, the former owner of the secondhand shop her mom now owns.