He couldn't bring himself to kill Darth Vader, however, because he continues to associate him with the Anakin he trained as a boy. This is also the exact reason why Obi-Wan didn't kill Anakin on Mustafar despite the opportunity a decade earlier in Star Wars: Episode III - Revenge of the Sith.
Obi-Wan knew it was only a matter of time. So, he made the difficult decision to use his learnings and become one with the force, rather than let Vader decapitate him.
During the scene, Vader explains to Kenobi that the latter will now suffer and that his pain is just beginning. Herein lies the reason why Vader doesn't want to kill Kenobi. Vader's dark side connection is fueled by his hatred and suffering, and a lot of that is caused by Kenobi himself.
One of the main plot points for the the Obi-Wan Kenobi Disney+ series is the revelation that Obi-Wan Kenobi does not realize that Darth Vader survived their battle on Mustafar and he only discovers he's still alive when he's informed by the Inquisitor Reva on the planet Daiyu while attempting to rescue a kidnapped ...
He can beat Vader easily. Ep6 shows that he knows definitively that he is a more powerful Force user and no longer has to fear Vader. He realizes that at any time he can take him out if he gets out of hand.
He slays Sidious and returns to Obi-Wan, begging for atonement by execution, only to be met with true forgiveness instead. But just as this fantasy Obi-Wan refuses to strike his former friend down, Vader refuses to turn his back on the dark.
Yes he did. And the saddest thing is that there was nothing he could do about it. He was broken. The first case is shortly after ROTS when Vader was making his Sith lightsaber.
Many have taken to the Internet to suggest that if it was really killing Kenobi that Vader was after, he simply could have brushed away the fire that followed to thwart his escape. And that is true. However, Vader is not just looking to kill Kenobi. He wants to make him suffer.
The short answer is yes, without a doubt, Vader regretted becoming a cybernetic monstrosity. First, there's the constant pain and discomfort from his suit. Worse, however, is the psychological pain. Vader destroyed everything he had ever known for a chance to save Padme.
Arguably, most Star Wars plot points revolve around characters simply not knowing something, very often about their family history. But, on top of all of that, the biggest reason Obi-Wan doesn't know Anakin is alive is that the last time he saw Anakin Skywalker in Revenge of the Sith, Ben literally left him for dead.
Before he discovered Vader had survived Mustafar, Obi-wan lived with the regret of killing his son, brother and best friend. After, he regretted not killing him and wondered if he had only made things worse by pushing Anakin further into dark side and Palpatine's arms.
Darth Vader showed no emotion at all when he killed Obi-Wan Kenobi. If you watch the scene carefully, you will see Kenobi pausing. He was letting Vader kill him. Whether Vader knew this at the time, or discovered it later, is an open question.
Although not fully explained on screen, Obi-Wan was killed in the physical sense, but he merged with the Force as what is known as a Force Ghost. In essence, the living energy of a person continues to exist after the body is no more.
While the theory seems quite plausible, Obi-Wan actually calls Anakin "Darth" in A New Hope because creator George Lucas hadn't yet established some elements of Star Wars lore. As the fictional universe expanded into the prequel trilogy, "Darth" became a Sith title as opposed to a first name.
Because we now know that it's not Obi-Wan's fault that Anakin became Vader—certainly not entirely. But it was Obi-Wan's doing, in very large part, that both of Anakin's children became the key heroic figures of the Rebel Alliance. He was the most important person in the galaxy, but not just for his failure with Anakin.
On Obi-Wan Kenobi, Darth Vader had been operating for ten years, making him 32 years old when he encountered his old Master, who had been hiding since Order 66. The pair fought twice, but it was during their second clash that Vader uttered a harsh truth.
Darth Vader didn't know about this particular skill because it was a practice that was long forgotten and was rediscovered by Qui-Gon Jinn. Given this, the Sith Lord couldn't believe that Obi-Wan vanished when he died — perhaps, even dubious at first about whether or not he's really gone.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
In the material around the film from the Legends timeline, it's established that by the end of Star Wars: Episode III - Revenge of the Sith, Kenobi was one of the characters who knew Anakin's Sith name was Darth Vader. However, what he didn't know was that he was still alive after Mustafar.
Can't Stand - Emperor Palpatine. Some would say that Palpatine represented Vader's only friend and companion, but real fans know that this is anything but the case. In many ways, Palpatine enslaved Vader and, over the years, Vader undoubtedly grew to resent his master.
Anakin does not have even the slightest bit of remorse. By the end, he feels nothing but anger. Although he feels regret for killing Padme, he still helps the evil Emperor. The film ends with Anakins standing side by side with the man on whose behalf he has committed all his crimes.
A very crucial scene in Return of the Jedi established that Obi-Wan Kenobi (a Force ghost by that point) blames himself for Anakin's fall to the dark side. He explained to Luke, “I took it upon myself to train him as a Jedi.