I could possibly see that if ben engaged him in a fight but not while his nephew was sleeping (thats how palpatine killed his master RJ is so clever lol), he cared about family especially leia to much to do that to her son. The whole reason she sent him to luke was to help ben cause snoke/palps had already got to him, she sensed a dark presence around her son, and hoped luke could help ben because he had already demonstrated he could help someone like ben- he was able to bring their evil father back to the light when no other jedi believed that was possible. If she thought luke was the type of person that would give up on ben so easily, and then even consider killing her son while he was sleepIng (sith style) she wouldnt have sent him there.
This is the same guy who refused to kill the most evil bastard in the universe who had committed horrible atrocities, so he wouldnt kill his nephew while he was sleeping cause he sensed darkness in him esp when thats the reason Leia sent ben to him to begin with. He already knew there was darkness in ben thats why ben was there. Ben had done nothing to act on that darkness as of that point, he hadnt killed anyone-its just not believable or consistent with lukes character at all.
More importantly he had already suceeded in turning vader back which should have reinforced his belief that he could help ben- all that he had learned about the darkside, tossing his saber aside cause he refused to kill or be tricked into killing his father. ?Young fool. Only now, at the end, do you understand?. He learned and then in tlj as yoda would say ?forget everything you have learned you did, untrue to yourself you were?
que doomcock gif force choking RJ, slamming his body into the ceiling, and slicing him in half with his saber all in one graceful motion