At Mistress Xiu's it wasn't just students who were fair game for elimination by classmates.
Taking out a teacher came with its own prestige at the academy; they were supposed to be leaders in the field of assassination, so terminating one was a guarantee to move up in the standings.
The teachers knew this made them targets though, and weren't above using each other as bait to find the most ambitious killers amongst their pupils and give them a taste of their own medicine...