The day Draco was caught by Potter in the restroom and nearly cut in half, he found his determination once more. That prat continues to stand in his way and he knew his mission would crush Potter’s spirit more than even the death of Sirius. But even so, it wasn’t that convincing of an incentive. Despite Draco’s arrogance and overall dislike of his nemesis, he never wished for Potter to die. At least not by the consequence of his own actions. Dumbledore is the gatekeeper for the safety of Hogwarts. He’d be putting the safety of his peers at risk with this mission. As he’s matured under his new circumstances, he couldn’t commit fully. Even though he was leaving this life behind to protect his family. To which Snape assured him of being a "noble thing".