You know what would have been great for that? If Harry tried to make amends with Draco during the Goblet of Fire or something, since he could die in one of these trials and he just wants to let Draco in on how he's a prick but he knows Draco was raised to behave like that. So he doesn't blame Draco as much as he blames Lucius. He dislikes Hermione because of her upbringing but it doesn't define her, etc etc. When Draco is inevitably faced with the choice to kill Dumbledore, he thinks back to the chance Harry gave him to be different. It isn't just about not killing someone because Draco was never that sort of boy, but Harry was the only person to actually tell him straight up that his mother and father brought this attitude and view of the world and it's wizards and muggles onto him. Had he met decent people sooner, things could be different. So Draco does it to not only stop himself from being a murderer, he also does it because he wants to believe Harry and believe that maybe he could still have pride and not go down the dark path he was groomed for. Then Severus steps in and you know the rest.

I know I shouldn't. Self-esteem--it's a bitch xD