Why was Anakin not suspicious about Palpatine knowing about Darth Plagueis?

Question

When Palpatine started revealing himself as a Sith Lord, Anakin's first words were to ask, "You know the dark side?"

Anakin appeared to be both surprised and suspicious at what Palpatine just said. However, Palpatine had expressed his awareness of the dark side and perhaps more suspiciously the Sith at a much earlier time, when he told Anakin about the tragedy of Darth Plagueis.

Why did Anakin not have a similar reaction at the time? In both instances, the matter of saving loved ones from death were not yet mentioned, so it would not have distracted Anakin yet.

Answer 1

This is covered in an earlier scene in the film's official novelisation. Palpatine claims that because the Jedi keep going on about the Sith, that he's been spending some time reading up on his history and has become quite the afficianado of Sith myths and legends. When he mentions the story of Darth Plagueis, Anakin is surprised to be hearing it, but doesn't immediately put 1+1 together, largely because he's a thicko distracted by worry about Padmé.

“The Sith are the definition of evil-“

“Or so you have been trained to believe. I have been reading about the history of the Sith for some years now, Anakin. Ever since the Council saw fit to finally reveal to me their … assertion … that these millennium-dead sorcerers had supposedly sprung back to life. Not every tale about them is sequestered in your conveniently secret Temple archives. From what I have read, they were not so different from Jedi; seeking power, to be sure, but so does your Council.” “The dark side-“

Anakin's later surprise was not that Palpatine knew about the mythos of the dark side of the Force, but that Palpatine was actually a dark Force practitioner, something that took him completely by surprise.

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Note that the scene above doesn't appear in the film which makes this a "legend", rather than part of the official Disney canon.

Answer 2

The later scene was Palpatine revealing that he was a force-wielder, rather than just someone with an unusual knowledge of history - that he knows how to use the dark side of the force, rather than just knowing that it exists

Answer 3

I believe that Anakin does suspect him, but his personal feelings get the better of him. (which is why he ended up turning to the dark side) At the time he is told the story about Plagueis and first learns that Palpatine knows about the Sith, is when Anakin is rejected a position by the Jedi council and also that he had been asked by Obi-Wan to spy on the chancellor had made him more distrustful of the council. On top of that he has also been having premonitions of his Padme's death and is intrigued by the story Palpatine tells him about Plagueis ,because it could be a means to save Padme. All of this just meant that he was willing to ignore his suspsions as his personal needs out weighed his loyalty to the Jedi order. Besides, the council knew that Palpatine was knowledgeable of the Sith. He had a wall carving of the battle between the Sith and the Jedi on Yavin IV before The Republic was formed in the Executive Office. The Jedi thought is was hung as a sign for reverence to their Order. But, it was to focus on Palpatine's true goal, the destruction of the Jedi Order, and the rise of the Sith.