What type of teacher doesn't fart in public?
A private tutor/tooter.
This is a pun! The joke plays on the similarity in sound between "tutor" (a teacher who works one-on-one with students) and "tooter" (a slang word for someone who farts). It's funny because it's unexpected and a bit silly, linking a formal role with something considered impolite.
Nonya
Approximately not an English as your first language joke site. 😬