Ben won’t kill Vader because he still considers Anakin his friend, he wants him to grow & gain the wisdom that Ben knows he’s capable of learning.
That still doesn’t work since he is adamant in Return of the Jedi that Luke must strike his father down, even going so far as to say when Luke says he can’t, “then the Emperor has already won.”
I’ve always disagreed with this interpretation. It’s always seemed to me that Obi Wan is telling Luke he has to be willing to kill him if it comes to it, not that he has to. It’s a question of his resolve. That’s why Yoda uses the word “confront,” he has to face his father again and go through a spiritual test of some kind to become a Jedi.
With that said that’s still not a good reason for Obi Wan not to kill Vader in this moment in the show. For that I just assume he can’t bring himself to do it, which is the same thing he had in Revenge of the Sith. He has pity in the same way Bilbo and Frodo have pity on Gollum.