Padme. Attacked by her husband on the Mustafar landing platform. Anakin, lost to the alure of the dark side, swayed by ambition, greed and most vitally fear of losing the one thing he cherished above all else - Padme herself. Lying on the Polis Massa medical table she turns to Obi-Wan and says her last words.
"There is still good in him... I know."
And there she dies.

Luke. Sitting with his sister on the forest moon of Endor. After all he has endured at the hands of Darth Vader, after the struggles and losses, mutilations and despair he tells Leia of their true heritage and then prepares to leave and face Vader.
"There is still good in him, I can sense it. I can save him, I can turn him back to the good side. I have to try."

Obi-Wan. Looking down at the burning body of Anakin Skywalker he lifts his lightsabre from the ashes of Mustafar and walks away, leaving Anakin to his death, unable to finish him himself.
"You were my brother. I loved you."

Three people, all connected to Anakin Skywalker, all hurt in different ways. But two of them were prepared to fight for his soul. One of them wanted Anakin dead.

Perhaps Ben, in the 19 years between Revenge of the Sith and A New Hope, had time to reflect on the folly of his uncompleted job. If he had finished Anakin,as Yoda instructed, then perhaps the years of Imperial rule might have gone differently. The Chosen One had turned to the dark side, and helped rule the galaxy through fear instead of help free it. By the time of Lukes emergence, perhaps Ben sees Vader as a separate entity from Anakin, who he still whistfully refers to as "A good friend."
Ben spins his yarn to Luke, of how a young Jedi named Darth Vader slew Anakin, through betrayal. While far too early to tell Luke the vast scope of the truth, he resorts to convenient lies, 'certain points of view', but words that enflame Luke's hatred for Vader. At this juncture, how could Luke ever believe that Vader was his father?

Come Empire, Ben is no more open to the possibility of Anakins redemption. He is against Luke leaving to save his friends, knowing it is a trap. Yoda, as cryptic as Kenobi, tries to persuade Luke to stay, but Luke is set to go.
But what are they afraid of? Luke getting into a fight? Certainly, Luke has had only limited training, but perhaps it is more than that.
Through the two trilogies, the 'bad guys' almost always tell the truth. Dooku told Kenobi the exact truth in Clones, Vader told Luke the truth on the Bespin gantry and Palpatine, while playing both sides into the middle and acting as leader of both, told versions of the truth.
'Certain points of view.'
But maybe Ben was fearful of Luke falling prey to the persuasive alure of the dark side. Or maybe the fact that Vaders words rang true to his son.
Luckily for Ben, the horror of Vaders reveal was too much for the young Jedi, who opted for death above possible temptation.

By Jedi, it is Luke who is pushing for answers, and using his powers to reveal more truths. Leia is his sister, Vader is his father, and Ben's words begin to unravel. Luke cannot bring himself to destroy Vader, and wants to bring him back to the good side, but Ben is unchanged.
"He's more machine now than man, twisted and evil."
Despite Luke seeing a kernel of goodness to redeem, Ben cannot accept the idea.
Perhaps, controversially, Kenobi belives Luke is the Chosen One, and in order for the Prophecy to be fulfilled Vader must be eliminated. If he still held faith in Anakin being the Chosen One, why train and encourage Luke to destroy him?

Which brings us to our opening point. If Padme and Luke could sense the goodness in Anakin then why couldn't Ben, who'd spent significantly more time with Anakin than either his wife or son?

Did Kenobi consider Anakin dead, slain by his own hands on the Mustafar lava shore?
Was separating the two the only way he could sleep at night, justifying the execution of a man he considered a brother?
Or was there something else?
Guilt?
Fear?
Or was Obi-Wan Kenobi hiding another secret?