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."
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.
He does. Right at the end. With Luke crying over him and Vader sensing his anguish and pain he had inflicted on all those who had cared for him.
Originally Answered: Did Ankain really care about Obi-wan during their time together? He has no problem fighting and trying to get rid of him on Mustafar. Absolutely. Anakin loved Obi-Wan like a brother, considered him a great friend, and a valued ally.
After defeating Darth Vader in the Obi-Wan Kenobi finale, Obi-Wan broke down and began tearing up when he saw Anakin's scars. It was the first time he had seen Anakin's face since leaving him to burn on Mustafar, and so he apologized for everything that had happened.
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.
First and foremost, Obi-Wan didn't want to have to confront and try to kill Anakin, we see this all the way until their final conflict in their duel where Obi-Wan pleads with Anakin to not make him do what he knows he'll have to do if Anakin tries to attack from the low-ground.
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.
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.
Vader responded “I am not your failure, Obi-Wan. You didn't kill Anakin Skywalker. I did.” This allows Obi-Wan to finally accept that Anakin is truly gone and that there was nothing he could have realistically done to save him.
Visions of Obi-Wan. The comic opens during the last moments of Revenge of the Sith, recreating the well-memed instance when a despondent, freshly-armored Vader cries out with a drawling “nooooooo” over how much he's lost.
Now we know why Anakin Skywalker said Obi-Wan was "holding me back!" “I'm really ahead of him.” In Attack of the Clones, Anakin Skywalker makes this casual boast about his master to Padmé Amidala and later, claims “It's all Obi-Wan's fault! He's jealous!
It is unclear whether Yoda would be more or less forgiving than Obi-Wan but one thing is certain - the former Grand Master would be ready to treat Anakin as an ally, following the events on the second Death Star. In Star Wars: Revenge of the Sith (2005), Yoda never really lost faith in Anakin in the way Obi-Wan did.
No. Her dying words were there is still good in him. Obi-Wan didn't tell her what happened after she lost consciousness on Mustafar.
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.
Obi-Wan knew Anakin through and through and understood his overconfidence and arrogance. He knew Anakin would fight with rage and aggression, while he remained cool and calculated. Pairing his understanding of Anakin with his knowledge of Soresu ultimately gave him the upper hand in the battle.
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.
He regretted it the moment he did it. He asked himself what he just did, dropped his lightsaber, and was visibly ashamed of himself when Palpatine anointed him a Sith Lord and began his speech about wiping out the Jedi.
"Goodbye Old Friend, May The Force Be With You"
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."
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.
The Tragedy of Anakin Skywalker was a Jedi history that detailed the fall of Anakin Skywalker. It gave full account of his romance with Padme Amidala, his desperation to save her that led to his fall to the dark side and the terrible deeds he committed in betraying the Jedi.
In Star Wars Legends and Canon, Galen Marek (Starkiller) is the only Jedi (other than Obi-Wan Kenobi) to put a beat down on Darth Vader/Anakin Skywalker. Galen was secretly trained as a Sith Lord apprentice to Vader, but returned to the light side and the Jedi.
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.