Some of the killing each other is part of the goal of being Sith'ari, the perfect being. If the apprentice is more powerful than the master, the master is killed. The apprentice becomes a master and takes an apprentice, apprentice gains more power, master is killed etc. Each time the apprentice gains more power than the last.
Here is a simple version of this:
Master1 teaches apprentice1 everything they know, apprentice1 learns and gains more power through their own experience and kills Master1
Apprentice1 becomes Master2
Master2 teaches apprentice2 everything they know, plus what Master1 taught them. Apprentice2 gains more power and kills Master2, becoming Master3
Master3 is more powerful than both Master1 and Master 2.
Master4 is more powerful than Master1,2, and 3
Master9001 is more powerful than all the masters before him.