Why won’t Edward let Bella hug Jacob in the very last chapter in New Moon?

Edward and Bella spend the majority of the novel apart; Edward believed that, in order to keep Bella safe, he had to end the relationship and erase himself from her life. Toward the end of the novel, Bella prevents him from exposing himself to the sunlight while in Volterra, which would have meant certain death by the Volturi coven. After this event, they vow to never be apart, as both are incapable of being without the other.
When Edward returns to Forks, he and Jacob have a confrontation. Jacob is Bella's best friend, and he is also in love with her. Edward can read Jacob's thoughts and recognizes this. Edward is protective of Bella and their love; as he has just reunited with her.