Obi-Wan isn't to blame for Anakin getting into the Jedi Order, but he is to blame for how he trained Anakin. At first, Anakin and Obi-Wan seem like the perfect match as Padawan and Master. Both are bold, headstrong Jedi who jump straight into action.
Throughout the fight, Obi-Wan knew that killing Anakin would "burn his heart to ash." He also expressed regret at the thought of the man Anakin could have become.
Anakin was one of the greatest Jedi warriors of all time, and yet Obi-Wan not only matched him, he ultimately defeated him. This victory, more than any other, has made Obi-Wan a legend – seen by many as the ultimate Jedi. And yet, surprisingly, Obi-Wan used the dark side to win both times he defeated the Sith.
The decision to train Anakin Skywalker as a Jedi ultimately led to the rise of the Empire and the destruction of the Jedi Order. However, Obi-Wan Kenobi's regret does not excuse Anakin's Skywalker actions. Anakin Skywalker was responsible for his own choices, and he ultimately chose to follow the path of 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.
The truth about Obi-Wan's failure and Anakin's fall
Why did Obi-Wan spare Vader?
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.
Anakin Hated Obi-Wan Because of an Imagined Relationship With Padme. Although Padme and Obi-Wan's affair couldn't have been further from the truth, Anakin apparently built up a scenario in his mind, which was only heightened by the Jedi Council's obfuscation in other areas.
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.
However, there is one other person who Darth Vader hates even more than his former master - and no, it isn't himself. Even before he fell to the dark side, Anakin Skywalker always held resentment for Obi-Wan.
As the heat began to consume Anakin, a grief-stricken Obi-Wan turned away, unable to watch his former Padawan and friend die. But Anakin lived. Rescued by Darth Sidious, he was encased in black armor and became known as Darth Vader, the Empire's brutal enforcer.
Because while Anakin is more powerful, Obi-Wan is more skilled. It's an extremely narrow skill gap, as we can see that they're almost evenly matched for most of the duel on Mustafar - but it's just enough.
And he's already murdered Mace Windu at Palpatine's behest, more or less by stabbing the Jedi in the back. 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.
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.
In Star Wars Legends Leia was visited by the force ghost of her father Anakin Skywalker, the man who used to be Darth Vader. It wasn't a pleasant meeting as Leia was unable to forgive him for the things he'd done no matter how hard he begged, and it was the only time she saw him.
Padme Amidala's secret marriage with Anakin Skywalker was one of the biggest reasons he eventually turned to the dark side. His emotions and love for her often clouded his judgment, and sometimes led him to be violent.
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.
On a very practical level, Vader could see that Obi-Wan had allies, and he probably sensed that there was a ring of Jedi supporters. If he captured or killed Kenobi right then, he would have had a much smaller chance of tracking down the other Imperial dissenters who were helping Jedi survivors.
After confidently claiming that he had far exceeded his former master in power, Vader was left mangled once more, screaming out the name that had been haunting him for the last ten years. Obi-Wan again proved himself to be far more capable and level-headed in combat than even Darth Vader himself.
