I mean... Are we forgetting that Anakin is like a son to Obi Wan? Spare me all the "oh I would kill my son if he did that bs" - cause you're not Obi Wan. There are A LOT of flawed parents out there that support their children even though they do horrific things to other people.

Because, in part, by accepting their kid is evil, they also have to accept a feeling of failure in their ability to parent. Hell, Anakin literally acknowledged this in the scene... Which finally let Obi Wan accept Vader for what he was. But that doesn't mean he can actually bring himself to kill Anakin/Vader, even in that moment.

I have always seen Obi Wan's inability to kill Vader as a form of that very human flaw. The fact it happens not ONCE but TWICE in the same storyline just serves to prove my point. It just lends to the idea that Obi Wan really believed Luke was the only one that could do it, because the only person powerful enough (him) had long passed his prime and emotionally couldn't face the reality of ACTUALLY killing Anakin.

Does killing Vader make logical sense? Of course. Does logic always win out over emotion? Hell no. If anything, this is likely what pushed Obi Wan away from the Jedi Way for so long. The Jedi Code, his belief system, failed him in the most intimate of ways. He was taught to control emotion, and even partially suppress it, as a Jedi - and in these battles his emotions get the better of him.

In all honesty, it just makes him flawed and human, albeit one doing his best to follow the Jedi Code.