While Castiel was resolved to kill Jesse and prevent any evil the boy might commit in the future, the Winchesters believed his human half gave him the capacity for good. Instead of killing Jesse, they gave him the chance to disappear. After Jesse's introduction in Supernatural season 5, he was indeed never seen again.
Azazel orders the assassination of Sam's girlfriend Jessica Moore, who was a distraction. Her death prompts Sam to return to hunting. Demons cannot be killed by conventional means so the Winchesters track down the Colt a mystic gun capable of killing anything in "Dead Man's Blood".
