Most people who teach music regard music teaching as an extremely rewarding career. There are so many instruments, styles and levels to teach. Music teaching has a rich and varied history (musical notation has been around far longer than audio recordings, enabling us to hear exactly the many beautiful compositions of Bach, Mozart, Beethoven and other great composers).
The feedback music teachers get from teaching music is also a great reason to pursue music teaching as a career. Playing through a difficult piece for the first time or feeling the buzz of being part of an orchestra is a feeling very few other subjects can instill in students.
Music is often regarded by students as a "fun" subject - like art or craft. Music teachers therefore rarely have to deal with the reluctance to learn experienced by math or science teachers.