I think it’s fair, in a sense, to say that Vader hates Obi-Wan by the time of ANH, but it’s also fair to point out that it’s not the only thing he feels for Obi-Wan, that it’s hate born of love, that it’s hate directed at himself just as much, and it’s hate that comes with a whole lot of obsession.
Anakin’s feeling about Obi-Wan are wrapped up in that Obi-Wan knows him, will always have known him, will always see what he’d done to become Darth Vader, who knew him while he was Anakin Skywalker, who saw the past of him just as much as he saw the present. Anakin could never look at Obi-Wan Kenobi without seeing the things he’d done, there was no way to ever forget the Jedi he’d murdered, the children he’d murdered, the entire worlds that he’d helped murder.
Even if Obi-Wan forgave him (and Anakin knew he would have), Anakin would still be reminded of it, because Obi-Wan was there for so much of his life. And Anakin Skywalker can’t bear to face what he’s done in a way that acknowledges that he was wrong, can’t bear to work through the pain of it, can only do so when he’s ready to let go of all of it, including his life, he never has to live with the guilt of it, and so he hates Obi-Wan Kenobi because Obi-Wan is a symbol of everything that Anakin Skywalker can’t face about himself.
But that doesn’t stop him from being obsessed with him–and you can feel that even in just the movies, where every time Obi-Wan’s name is mentioned, it’s because Anakin brought him up out of nowhere in the conversation.
There’s so much that Anakin is revolving around and putting into context through Obi-Wan, despite that Luke isn’t the one who brings him up.
This is furthered in the comics, too! In Dark Lord of the Sith (the Charles Soule comic, which I’m only not quoting everything of to keep this post to almost a reasonable length! 😂) the arcs of the story are all basically structured around Anakin rejecting the idea that he could have taken another path. He kills Jocasta Nu because he could have gone down the same path as her. He kills Eeth Koth because he could have gone down the same path as him. He kills Feren Barr because he could have gone down the same path as him. (Soule has even commented on how the focus was on that Anakin was too afraid to face what he’d done.)
He even literally has a vision put into his head by the Force or the kyber crystal that he’s bleeding, that shows he could go kill Sidious and beg Obi-Wan for help (or to kill him) and the vision shows that he knows Obi-Wan would have listened to him and turned off his saber:
This is issue #5 of the run and it’s one of the absolute most important moments to understanding Anakin Skywalker as Darth Vader in my opinion. That his eyes are blue when he has his vision, that he is shown to be clear-headed from the dark side for a brief moment. That he understands that he had options and people would have helped him, that there were other paths.
And that he specifically chooses to reject it. “No. I refuse. This is all there is.”
This is also fundamental in showing that Anakin’s hate for Obi-Wan is coming from a place of knowing that Obi-Wan would have helped him, that Obi-Wan loved him.
Which is evidenced again and again in the comics as well, how he keeps bringing up Obi-Wan’s name, even “talking” to him, because Anakin cannot let go of him:
Anakin also has had MORE THAN ONE thought about that day on Mustafar and it always gets shown that he includes the moment where Obi-Wan says he loved him:
Sometimes Anakin is the one on fire, screaming at Obi-Wan, who tells him he loved him. Sometimes Obi-Wan is the one on fire, still trying to tell Anakin he loved him.
Anakin’s hate for Obi-Wan is born out of how much Obi-Wan loved him, how much Obi-Wan probably still loves him, and that some part of Anakin misses that and wishes he could go back, but he cannot face who he used to be by anyone who actually knew him, the way they would look at him was too much for Anakin to bear.
Even when he finally kills Obi-Wan, there’s no satisfaction in it for him, no relief from the hate and loneliness for him:
(”There Is Another” by Gary D. Shmidt)
You don’t fall into a painful loneliness so deep that Yoda feels it halfway across the galaxy and even after you literally murdered all the grandbabies, he still almost feels bad for you because it’s so deep a loneliness, not if you don’t still love that person.
You don’t talk to their lack of presence in your life if you don’t still love them, even if you hate them, too. You don’t bring their name up in conversation if you’re not thinking about them, which you don’t do if you don’t love them just as much as you hate them.
Anakin hated him, but it was hate born of how he couldn’t stop loving Obi-Wan, how he couldn’t stop missing him, couldn’t stop hating the path he’d forced himself onto and never being satisfied there, but also never being able to let himself go back.