Does the tail have any meaning?

There's a teacher in the "Rosario + Vampire" series on Netflix. She is a cat and has a tail (cats tail). And sometimes the protagonists would say the teacher her tail or something in the direction. The teacher was always ashamed of it. I really have no idea why that is, or do I just have no sense of humor?

The teacher is a bakeneko.

There's a rule at school that you are not allowed to show your "yokai" shape

More on Kazuma's side in this regard.