This Star Wars Theory May Explain Why Obi-Wan Let Darth Vader Live (It Wasn't Mercy)
"Obi-Wan Kenobi" on Disney+ was more than an excuse to get Ewan McGregor back in a Jedi robe. It helped fill in some blanks connecting the prequel trilogy to the original. Obi-Wan (McGregor) actually knew Princess Leia (Vivien Lyra Blair) when she was a child, and he battled Darth Vader (Hayden Christensen) a long time ago. In fact, if Obi-Wan wanted, he could've killed Vader right then and there but opted not to. Seeing how Vader killed Obi-Wan in "A New Hope," this may come across as a foolish act on the Jedi's part, but some think there's more than meets the eye.
Redditor u/Eicho3 posited ideas on why Obi-Wan didn't kill Vader when he had the chance. For starters, it wasn't the Jedi way to kill an opponent at the end of a duel, similar to how Obi-Wan didn't want Anakin to kill Count Dooku (Christopher Lee) in "Revenge of the Sith." However, another explanation may be found in the prophecy that Anakin would bring balance to the Force: "He feels it in his bones that Qui Gon was correct about the prophesy, and that Vader/Anakin is on a journey, potentially to end the Sith forever, but sadly, this is the path it must take."
While Obi-Wan may have wanted to show Count Dooku mercy, he adopted a more practical approach with Vader. It may break his heart to see his Padawan go to the Dark Side, but by the end of "Obi-Wan Kenobi," he realizes this is the way. He knows a lot of suffering will transpire, but it's the only way for Anakin to defeat Emperor Palpatine (Ian McDiarmid). He's come a long way from "Revenge of the Sith."
Obi-Wan Kenobi trusts in the Force by the end of the series
"Revenge of the Sith" leaves Obi-Wan Kenobi as a broken man. This is best exemplified in his line to Anakin at the end of their fight on Mustafar. The internet may have turned it into a meme, but it shows how he no longer believes in the prophecy: "You were the chosen one! It was said that you would destroy the Sith, not join them! Bring balance to the Force... not leave it in darkness!" It can be inferred that Obi-Wan had a different reading of the prophecy than what actually took place, but by the end of "Obi-Wan Kenobi," he realizes it still holds true.
When the series begins, Obi-Wan has cut himself off from the Force. It makes sense; after believing the prophecy and the will of the Jedi failed him, he likely wanted to stay hidden. However, throughout the show, he realizes his work isn't done yet, and he'll have to go back to trusting the Force to bring peace to the galaxy. Redditor u/Eicho31 points out how Obi-Wan is changed in the final episode, "You can see that surrender throughout the second half of ep6 – he's calm and cool, telling Lars the future will take care of [Luke] and feeling at peace, finally. He can trust in the Force." This physically manifests when Obi-Wan sees the Force Ghost of Qui-Gon Jinn (Liam Neeson). He's going back to his Jedi teachings because the prophecy can still be fulfilled.
Throughout much of the prequel trilogy, Obi-Wan believes Anakin will bring balance to the Force. He may have initially viewed this as Anakin being the one to defeat the Sith, but as tends to be the case with prophecies, it doesn't always pan out how one expects. So at the end of the show, Obi-Wan leaves Vader alive because he no longer tries to bend the Force to his whim. He gives into a greater power and trusts the prophecy will still transpire.