Why must Harry Potter be told that a part of Voldemort's soul latched itself onto the only living thing it could find, again?

In Severus's memory, he and Dumbledore have a talk about Harry Potter.

Professor Albus Dumbledore: There will come a time when Harry Potter must be told something. But you must wait until Voldemort is at his most vulnerable.

Professor Severus Snape: Must be told what?

Professor Albus Dumbledore: On the night Lord Voldemort went to Godric's Hollow to kill Harry, and Lily Potter cast herself between them, the curse rebounded. When that happened, a part of Voldemort's soul lached itself onto the only living thing it could find. Harry himself. There's a reason Harry can speak with snakes. There's a reason he can look into Lord Voldemort's mind. A part of Voldemort lives inside him.

This quote was found on IMDB, and I do believe it is the movie edition. I also believe that this happened in the books as well. (If not, and edit would be much appreciated)

In Harry Potter and the Chamber of Secrets (book), Dumbledore has already told Harry that a part of Voldemort was in Harry.

Dumbledore: Unless I'm much mistaken, he transferred some of his own powers to you the night he gave you that scar. Not something he intended to do, I'm sure...

Harry: Voldemort put a bit of himself in me?

Dumbledore: It certainly seems so.

Harry was already told that some of Voldemort was in himself. Why did Dumbledore ask Severus to tell him again? Was is because he added that Harry must die?

Why must Harry Potter be told that a part of Voldemort's soul latched itself onto the only living thing it could find, again?