Why does snape make an unbreakable vow?

(WARNING: SPOILERS) Rowling never makes it expressly clear in any of her books. However, it is likely that Snape already knew that he would be the one to kill Dumbledore. This, after all, is what Narcissa pleads him to promise: That Snape will watch over Draco, that he will intervene if necessary to secure his saftey, and that, if Draco fails to kill Dumbledore, that Snape will do it for him. Now, obviously Snape knows, since he is on Dumbledore's side, that Dumbledore wouldn't ever hurt Draco or put him in harm's way. So that he could honestly promise Narcissa with little problem. Also, because he promises to kill Dumbledore should Draco fail, we can assume that he has already had the conversation with Dumbledore that deals with Snape bringing about Dumbledore's death when the time comes. This allows him to promise truthfully that he will kill Dumbledore. Snape also has a certain prejudice in Malfoy's favor, since he happens to be an exemplary Slytherin student and is good at potions (though this may well be due to grade inflation). Of course he promises to keep his favorite student safe: but what Narcissa doesn't know is that Snape is not agreeing to protect Draco from Dumbledore and the Order; rather, he's agreeing to protect Draco from Voldemort and from bringing about his own downfall. We see Draco's attempts to throw Snape off his track and to get him off of his back throughout the sixth novel, but know that Snape ultimately succeeds and keeps Draco (as) safe (as he can) from "The Dark Lord".