No he wasn't forgiving him. Vader or Anakin was backed into a corner. He had clearly lost this final duel with Obi-Wan. His desire for revenge against him caused him to make the same mistakes he made when dueling Obi-Wan in the past.
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.
While Anakin Skywalker is ultimately reawakened by the love of his son, Darth Vader is relentless in the disdain and loathing he holds towards his enemies - none more than Obi-Wan, who struck him down on Mustafar, leading to Palpatine rebuilding him as his cyborg servant.
But in a strange moment of comfort, Darth Vader took much of the weight off Obi-Wan's shoulders. He told him, “I'm not your failure, Obi-Wan. You didn't kill Anakin Skywalker. I did.” We saw later in the original trilogy, on some level Ben still believed he bore some responsibility.
“I am not your failure, Obi-Wan,” Vader says. “You didn't kill Anakin Skywalker. I did.” With that closure, Obi-Wan is able to walk away from the encounter, acknowledging his old friend as “Darth” and leaving his attachment to Anakin behind.
In Episode III, just before they are to set off on their respective missions, Obi-Wan and Anakin share a farewell. Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master.
The added risk Darth Vader takes in allowing children to live in a situation where he could have killed them proves that he regrets killing Younglings and will avoid harming any more children for the rest of his days, though intense intimidation is a dark strategy to avoid repeating his Youngling massacre.
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.
Darth Vader hated Obi-Wan Kenobi because he hated himself. This started when he thought that Kenobi was the one that poisoned Padmé into turning against Anakin when he turned to the dark side.
Of course, Obi-Wan didn't finish Anakin off ten years ago on Mustafar because he didn't want to be the one to strike the killing blow on a man that he loved like a brother.
The answer is seeming, simple: Obi-Wan's self-imposed isolation also includes a news blackout. Not only does he not spread information about himself around, but, he also doesn't appear to take in any new information about what's going on in the galaxy.
But Obi-Wan Kenobi's finale helped make Ben's case. 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.
Darth Vader is Clearly the More Powerful Force User
Between Darth Vader and Obi-Wan, it's pretty clear that Vader is far more powerful with the force. After all, he pretty easily used the force to stop a starship from taking off in the previous episode, and manhandled Kenobi throughout the majority of the show.
He also had no lover for a few reasons, he would never get over Padme she was to much to him. He was in a massive black suit that was probably fairly intimidating to women he also had a reputation of force choking those who displeased him. Probably not high on anyone's Valentine's Day list.
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.
David Porter provides some great philosophical context to why Obi-Wan would not regret leaving Anakin alive, as it was obviously “the will of the Force” that Obi-Wan be unable to finish him off, and “the will of the Force” that Anakin live on to kill Sidious himself in the future.
It's not shown, but it is clearly insinuated that Anakin killed the younglings. This is confirmed later in the movie when Obi-Wan informs Padme that Anakin killed them. Both are torn apart with hurt and confusion, trying to make sense of something so terrible. How could Anakin do such a thing?
As we know, Vader was killing children before he even got his suit on, but those were Jedi younglings and so future potential threats. Vader doesn't kill right and left just to be “evil.” A random kid hugging him would presumably be brushed rather brusquely aside, but that would be all.
Did Anakin regret choking Padme? Oh yeah. He pushed the memories out of his mind for a couple of decades. But after he faced his son, Luke, in Empire Strikes Back, it was all he could think about.
He explained to Luke, “I took it upon myself to train him as a Jedi. I thought I could instruct him just as well as Yoda. I was wrong.” His guilt was apparent in Revenge of the Sith, when he explicitly told Anakin in the heat of their duel on Mustafar, “I have failed you, Anakin.
We go for the more simple answer, further considering the details of the question itself. If Anakin didn't go into that chamber as the Jedi confronted Palpatine, then Mace Windu would have defeated Palpatine, killing him. If you remember, Mace had him. He was ready to kill him.
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.