The real family was always worth fighting for. In his previous life, after he lost his family completely, loneliness slowly ate away at him from the inside. Here, all he had right now was Sansa. She had been through many things and was sometimes still a bit foolish, but she was family, and Jon wouldn't trade her for the world. There was this fear in his head that if Sansa learned about his magic or his terrible deeds, she would be terrified and disgusted and keep her distance and avoid him, just like his original cousins, the Dursleys. This irrational fear made him hesitate in telling her; that and the fact that there were people within hearing distance nearby, including Brienne of Tarth.