How we cite our quotes: All quotations are from Harry Potter and the Half-Blood Prince.
Quote #4
SNAPE: I swore to protect you. I made the Unbreakable Vow.
MALFOY: I don't need protection. I was chosen for this. Out of all others, me! And I won't fail him.
SNAPE: You're afraid, Draco. You attempt to conceal it, but it's obvious. Let me assist you.
MALFOY: No! I was chosen. This is my moment.
Harry might be the "Chosen One" who's headed for a date with destiny (i.e., killing Voldemort), but Draco is feeling just as locked in to his own fate. Sure, it sounds like he's getting a little bit of an ego boost from the fact that Voldemort singled him out for this mission, but he's also kind of trapped, right? Once Voldemort asks you to do something, you'd better do it, or something pretty nasty is going to happen.
Quote #5
HARRY: So, what happens to you? What happens if you break an Unbreakable Vow?
RON: You die.
[The scene changes.]
LUPIN: Voldemort has chosen Draco Malfoy for a mission?
HARRY: I know it sounds mad.
LUPIN: Has it occurred to you, Harry, that Snape was simply pretending to offer Draco help so he could find out what he was up to?
Speaking of choices and things you can't get out of: Snape has made an Unbreakable Vow to help Malfoy out with whatever mission Voldemort has assigned to him. If he fails? He dies. So, yeah, it sounds like he really doesn't have much of a choice if he wants to survive to help…well, whichever side he's actually helping.
Quote #6
HARRY: I'm going to tell you something. Something others have only guessed at. It's true. I am the Chosen One. Only I can destroy him, but in order to do so, I need to know what Tom Riddle asked you all those years ago in your office, and I need to know what you told him.
Ah, so finally, Harry admits it out loud: He is the Chosen One. However, until he gets the full 411 on Voldemort's relationship with Slughorn, that knowledge isn't doing anyone any good. He may have been "chosen" to defeat the Dark Lord, but he needs to figure out, well, how.