During their confrontation on Mustafar, he was heartbroken seeing what happened to Anakin. Even when he had the chance to end him then and there, the Jedi Master couldn't bring himself to kill him. So instead, Obi-Wan left him limbless, not expecting Palpatine would come to rescue his fallen Padawan.
Obi-Wan Left Anakin Because He Sensed Palpatine Approaching
Stover revealed that Obi-Wan had multiple reasons to kill Anakin after their duel. Yoda had told him that he needed to kill his former Padawan to put him out of his misery after his fall to the dark side.
Obi-Wan Kenobi recognized that he had options, such as providing Anakin Skywalker more time to mature prior to beginning his Jedi training. He also admitted that he was too focused on turning Anakin Skywalker into an elite warrior, instead of nurturing his emotional intelligence.
Before Anakin's leap, Obi-Wan warned him not to engage further, but Anakin underestimated Obi-Wan and the power of the high ground. Even if highly unconventional for a Jedi, Obi-Wan saw no other option than to put an immediate stop to Anakin and dismember him.
Though Obi-Wan was often an important ally for Anakin, the young Jedi could never see past his envy, even going far enough to allow himself to believe that his master was having an affair with his wife. In the end, Anakin's own jealousy was his undoing and the reason that he would never surpass his master.
GEORGE LUCAS SAYS OBI-WAN WAS TO SAVE ANAKIN ON MUSTAFAR
Did Anakin regret betraying Obi-Wan?
After his redemption, after bringing back balance to the force, after the return of the Jedi, Anakin would have definitely held a bit of remorse, not to forget, it was Obi-wan who taught Anakin how to become a force ghost, to stray oneself from the cosmic force and assume identity with the living force.
Star Wars Explained - A long time ago, in a galaxy far, far, away... Why didn't Yoda train Anakin Skywalker if he really thought that he was "the chosen one"? Yoda didn't want Anakin trained. He considered him to be dangerous, full of fear which could potentially be catastrophic.
Yes, when Darth Vader turned back to Anakin Skywalker and sacrifice himself to save his son, he dies and Obi-Wan uses the force to connect with Anakin's spirit. In that time Anakin apologizes to Obi-Wan, desperately asking him to forgive him for everything he has done to him and everybody over the years.
The fact that Anakin was so powerful was in itself, a problem, because some Jedi viewed him as a potential threat to the Jedi Order, like Mace Windu for example, Master of the Order, was suspicious of anyone he perceived to be a threat to the traditions of the Order.
It's strongly implied in “The Rise of Clovis” episode of The Clone Wars show that Obi-Wan is aware of Anakin's relationship with Padmé, or at least his feelings for her. The Obsession comic basically confirms he knows, too.
During the slaughter scene, we see Anakin crying whilst killing the separatist. This is because Anakin is. not yet fully committed to the dark side. and has now realized through his actions.
If we go by the need to rationalize what we saw, Obi Wan either felt Anakin deserved to die in pain over however long it would take, or didn't really want to kill him. The obvious reason is that Anakin needed to survive in order to become Darth Vader.
Return of the Jedi establishes that Yoda was aware that Anakin Skywalker had fallen to the dark side and become Darth Vader. When questioned by Luke Skywalker, he confided that Anakin was Darth Vader. Later, Obi-Wan Kenobi's Force ghost confirmed that Anakin had indeed fallen to the dark side and become Darth Vader.
With Yoda's presence in the Force cloaked, there really wasn't any way for the Empire, Darth Vader, or Vader's Inquisitors to find the Jedi master. Another potential explanation is the planet Dagobah itself.
The canonical comic Star Wars: Darth Vader #7 confirms the younglings' deaths caused Anakin grief, self-loathing, hatred, and pain, fueling his descent even further into the Dark Side.
And all the way up until the third sister told him otherwise, Obi-Wan truly and completely believed that Anakin was dead. He believed that he died on the banks of Mustafar. And even if they knew for a fact the Anakin had survived, it comes back to the split personality.
On a practical level, Obi-Wan did not know that Anakin had survived simply because he was isolated on Tatooine. Although Obi-Wan did not see Anakin die after their battle on Mustafar in Star Wars: Revenge of the Sith, he reasonably could have assumed that Anakin would die from his injuries.
Darth Vader did not 'forget' he was Anakin. He believed he was not Anakin Skywalker; a completely different person whom he killed. You will read in EU materials, that he referred to his memories as Anakin, as 'The Jedi'. He suppressed most of Anakin Skywalker's memories - his memories while he was Anakin.
This fell in line with various fan theories and non-canon novelizations that suggested Obi-Wan and Padmé had an affair sometime during the Clone Wars. In the Star Wars prequel movies, Obi-Wan often has a duty to protect Padmé, but there was never any sense of romantic feelings.
Having been completely and utterly defeated during their first battle in Revenge of the Sith, Darth Vader harbored a grudge against his former master which fueled his hatred for many years. Obi-Wan Kenobi's third episode confirms Darth Vader's biggest mistake came when he had a chance to finish the job.
