Another reason could be personal vengeance. Maybe there was some past incident between them that we don't know about from the official Star Wars lore. Lord Kahn could have held a grudge against Darth Bane for a long time, and finally, when the opportunity arises, he takes his revenge by killing him.
One possible motivation could be a power struggle. Maybe Lord Kahn sees Darth Bane as a threat to his own rise to ultimate power within the Sith hierarchy. Bane is known for his Rule of Two, and Kahn might want to break free from that and establish his own dominion, so he eliminates Bane.
It could also be due to a difference in ideology. Darth Bane has his specific views on the Sith way, and perhaps Lord Kahn has a different vision for the future of the Sith. Kahn may believe that Bane's methods are holding the Sith back or are too traditional, so he decides to kill him to pursue his own path.