Sword Art Online's Akihiko Kayaba is a difficult man to understand. He's responsible for creating a death trap out of his own VRMMORPG, but even he cannot pin down a concrete reason for doing so. He has since appeared intermittently throughout the series to help out the main cast.
Kayaba's role in the series changes as he sees fit. Usually, he seems content acting as a simple observer of the exploits of the main characters. However, there are times when he chooses to take action and intervene in important yet unusual ways. In the latest season of Sword Art Online, for instance, he possesses an AI robot to save his former lover. All the acts he has committed over the course of Sword Art Online, good or bad, bring his character into question, making fans wonder whether he was ever really a bad person or if he's worthy of forgiveness. Evaluating this requires a closer look at his most significant acts within the story.
Kayaba's biggest contribution to the Sword Art Online narrative is his eponymous VR game. He succeeds in trapping 10,000 players in the virtual world of SAO. Once there, players run the risk of dying by either getting a game over or having someone in the real world try to remove their VR headset. Through his game, Kayaba becomes responsible for 3,853 deaths. This is important in judging him as a person because whatever good anyone can say about him will have to be followed by "but he still killed those people."
Kayaba's next act in the series comes in the climax of the Fairy Dance Arc. As the series protagonist, Kirito finds himself helpless before Oberon the Fairy King and his admin privileges when Kayaba (or rather, his computerized memory) arrives to provide him with the support he needs. He gives the fallen hero a much-needed pep talk as well as the administrative power necessary to beat Oberon and save Asuna. When the fight is over, he also gives Kirito the World Seed, which allows him and anyone he shares it with to create their own VR worlds. Kayaba's assistance not only helps Kirito, but also leads to a significant advancement in virtual reality and game design. But he still killed those people.
Kayaba doesn't get another major role until much later in the series. Near the end of the Alicization Arc, he takes control of an AI robot to disarm some bombs. In doing so, he saves Kirito, his friends and his former lover Koujiro Rinko. But he still killed those people.
Kayaba will never be able to fully atone for the thousands of deaths on his hands. However, his actions following the first arc aren't necessarily about redemption. Instead, his goal seems to be to aid in the progression of virtual reality. His true purpose is and always has been to blur the line between fantasy worlds and the real world.
Kayaba's dreams of such a merge fit with his actions throughout Sword Art Online. A possible explanation for making SAO a death game would be to make the game seem more real with higher stakes. When he gives the World Seed to Kirito, he does it with the hope that it will be used for at least one more VR game like SAO. Similarly, when he saves his former lover Rinko, it's so that she can carry on his dream to merge fantasy and reality with her FullDive technology research. Progressing the field of virtual reality seems like a goal consistent with all of Kayaba's appearances and actions.
Akihiko Kayaba isn't necessarily meant to be forgiven, but he is meant to be understood. His reasoning for making SAO so dangerous in the first arc is difficult to decipher. However, as he continues to make appearances in the story, he becomes more fleshed out and his motivations become clearer. Whether or not he can be forgiven is ultimately left up to the judgment of those he's responsible for hurting and the audience. The fact that survivors of the original SAO still play it suggests that they at least have learned to let go of their contempt for Kayaba.
