Dumbledore lying to Snape about Harry's final task

[Miles]

No: HPFGUIDX 172424

"So the boy... the boy must die?" asked Snape, quite calmly.
"And Voldemort himself must do it, Severus. That is essential."
Another long silence. Then Snape said, "I thought... all these years ...
that we were protecting him for her. For Lily."
"We have protected him because he has been essential to teach him, to raise
him, to let him try his strenght," said Dumbledore. (...)
"You have kept him alive so that he can die at the right moment?"
"Don't be shocked, Severus. How many men and women have you watched die?"

Dumbledore does not tell Snape the real plan. He tells him that Harry really
has to die, and that he had planned this for years. As we learn later,
Dumbledore expected Harry to survive Voldemorts Killing Curse. Why didn't he
trust Snape to know the truth?

First of all, it WAS necessary that Harry thought there was no other way.
That made him face Voldemort wandless - otherwise there might have been a
real fight, and he could have been hit by a curse from any DE, with fatal
consequences. Only an AK from Voldemort himself would do the trick. But why
not tell Snape?

Several answers:

a) It was necessary for the plot. Snape giving Harry the information the way
he did, there would have been no way to change it for the pensieve.
Not a good answer, there were different ways for JKR to tell the story.

b) Dumbledore expected that Snape would have to give Harry the final
instructions via the pensieve.
That's possible, but Dumbledore was not a Seer. To foresee that kind of
circumstances would stretch DD's abilities a bit, so I don't like the
answer.

c) Dumbledore didn't trust Snape's feelings towards Harry.
I think this answer could be part of the truth. Dumbledore heard many
complaints about Harry from Snape over the years, so he might have
considered the story about Harry being just a tool (not a human being) to be
more comfortable for Snape to hear. Dumbledore himself pretended not to care
about the boy, so Snape could join him.

d) Dumbledore wanted to see Snape's reaction.
This answer can be combined with c). Obviously Snape did *not* like treating
Harry as a mere tool. He saw him as Lily's son, the son she died protecting,
so he felt responsible to protect him himself.

Even implying c) and d) as possible reasons for Dumbledore, I'm not
comfortable with Dumbledore not trusting Snape here.

By the way - in his last moment Snape wanted to see Lily in Harry, not James
as always before - that's why he asked Harry to look into his eyes.

Miles