"I can't do it, R2," Luke said to the droid that had always been there for him. "I can't go on alone."
"Yoda will always be with you," came Obi-Wan's voice. Luke looked around and saw Obi-Wan in blue spirit form.
"Ben! Why didn't you tell me?" Luke said. "You told me Vader betrayed and murdered my father."
"I didn't know, I thought what I said was true," Obi-Wan said.
"How can you not know the difference between 'Betrayed and murdered' and 'Is the same person as'?"
"When your father was seduced by the dark side, it was as if he became a different person--"
Luke turned away in disgust, "That's your excuse!? That he's a different person now?"
"No, Luke. Please allow me to explain."
Luke turned back, "Fine."
Obi-Wan sat on a log and gestured for Luke to sit beside him. Luke didn't.
"Anakin was a good friend," Obi-Wan said. "When I first knew him, your father was already a great pilot. But I was amazed hos strongly the Force was with him. I took it upon myself to train him as a Jedi.
"He was my first, but soon I had three students: your father, your mother, and Darth Vader. I thought I could instruct them as well as Yoda. I was wrong."
"But Darth Vader is my father," Luke said.
"No, Darth Vader is dead," Obi-Wan said. "He did betray your father, as I told you before, and he did attempt to murder him. After the battle the only survivor was mangled and burned beyond recognition. When the Empire's servants came, he introduced himself as Vader and has used the name ever since."
Luke finally sat down beside Obi-Wan.
"I assumed that Vader had succeeded in killing your father. I was wrong. I encountered him several times after that, as the Clone Wars drew to a close, and not once did I sense he was really Anakin. The dark side had twisted him until he was unrecognizable."
"There's still good in him," Luke said.
"Has he ever shown it, Luke?" Obi-Wan asked. "I wouldn't have sent you to live with your Aunt and Uncle if I'd know the man calling himself Darth Vader was actually Anakin Skywalker because it placed you at risk.
"To keep our families safe, we never spoke of where we came from. Only Anakin and I knew about Beru and Owen so I assumed you'd be safe there. Skywalker is a common enough name near Tatooine.
"But I was wrong, and you were at great risk. What if Anakin had stopped in to see his family and discovered you? Imagine being raised by Darth Vader if he took possession of you, or he might have simply killed you to avoid a potential future threat.
"But it never happened. He never looked up his family, he has never shown love, he has murdered people without hesitation or guilt. What good could be left in him?"
*silence during which Luke is uneasy*
"And my mother?" Luke asked.
"The Emperor knew as I did that if Anakin were to have any offspring they would be a threat to him, even more so since your mother was a Jedi too. So when she became pregnant I arranged for her to go into hiding. By the time you were born the war was over, and we had lost.
"She wanted to raise you, but the Jedi purges continued after the war, and there was a chance she might be found, so to keep you safe she had me take you to Anakin's family. That's what she told me, at least.
"She died --of natural causes-- a few years later. I'm sorry I don't have better news for you.
"You should know that Yoda did plan to tell you about your father, when he felt you were ready for such devastating news. You left before then."
"I know how shocked and hurt I was when Yoda told me the truth. The pain was worse than when I died.
"But right now, what matters is that Anakin and the Emperor are still out there. Your friends experience with Anakin should prove to you that they cannot defeat him on their own."
"I can't do it, Ben," Luke said.
"You cannot escape your destiny," Obi Wan said. "The future is always in motion, but certain future events are fixed in place. You must face Darth Vader again."
"I can't kill my own father!" Luke shouted.
"When was he there for you?" Obi-Wan asked. "He killed Beru and Owen. The Anakin I knew would never do that. He loved them both too much. But he did. He killed the people who raised you. He's changed Luke. He's nothing like the man who loved your mother. He's nothing like the man who constructed a new lightsaber in the middle of a war just so he could bequeath his original one to you. He's nothing like the man who would have loved you."
"It doesn't matter," Luke said quietly. "I can't kill my own father."
Obi-Wan hung his head. "Then the Emperor has already won. You were our only hope.
Luke remembered something, "Yoda spoke of another."
"Yes, another of the surprises Yoda had for me," Obi Wan said. "But it is a secret best kept."
"He said there was another Skywalker," Luke said. "I think I deserve to know about my own family."
Obi-Wan sighed, "I was told that the reason your mother delivered you into my arms to bring to live with Beru and Owen was that she was afraid of being found in the ongoing hunt for Jedi, and that concern was true, but there was another reason.
"You are one of twins."
Luke was too shocked to say anything.
"Yoda felt that it would be safest if you were separated. You were sent to live with your father's family, your twin sister remained with your mother. Because of your mother's death, even your sister doesn't know her heritage, and it is best that way. Her anonymity has protected her since her birth."
Luke thinks about this and then his eyes light up, "Leia! Leia's my sister."
"Your insight serves you well," Obi Wan said. "Bury your feelings deep down, Luke. They do you credit, but they could be made to serve the Emperor."
Or something like that.
When looking up the canon conversation I found this:
Oh, hey, a less cynical one (only Obi-Wan's Star Wars description, not RotJ certain point of view):