There's nothing that says that. The teachers' private lives are not discussed, by and large. We don't know if, say, Flitwick is married or not.
Exactly the point I was going to make... I seem to recall some comment from Rowling in an interview that not all the teachers live at Hogwarts (easy to commute in from Hogsmeade, after all, and not everyone eats at the Head Table). Nothing says there’s no Mr. Sprout or Mrs. Flitwick back home.