Three Sentence Ficathon

I think it's thanks to a combination of factors. It helps that Obi-Wan can actually focus on Anakin instead of "heavily pregnant civilian in mortal danger", so he can see the tiny spark of Anakin buried deep inside Vader. Him not being willing to kill Anakin is also very Jedi; he's not killing an enemy unless he has to, which, in canon, is a part of why he leaves Anakin/Vader to burn, but here, it means he's determined to bring him back or die trying. There is also a part of Obi-Wan that still loves Anakin, and killing him would devastate him despite the circumstances; but if he's not killing Vader, then bringing him back to the Light is pretty much his only available option and Obi-Wan recognizes that.