Upvote:6
To preface my answer, not all Church policy is shaped by doctrine. Some policies are practical.
That said, I don't know why this is the case, but the handbook does say:
12.2.2. Ward Sunday School Presidency
Members of the ward Sunday School presidency are priesthood holders.
Also, speaking of the ward Sunday School president:
He also oversees the calling and setting apart of other Sunday School workers. He may assign his counselors to call and set them apart.
This, of course, requires the priesthood to do.