It’s more like “someone who’s talking behind your back”, quite literally, because “Fotzn” is just Bavarian dialect for “mouth” that has really nothing to do with female genitalia. I also don’t think it’s hugely offensive and a lot of people use the term Fotzn in various ways pretty casually in Bavaria and Austria.

That said, it’s still a pretty weird thing to say for a teacher though, that’s for sure.