Again, Bella is a private person (and in some ways a typical teenager), and she’s not ready to let Charlie in on the fact that she’s romantically involved with Edward. But for Edward, this poses a bit of a problem. He has to carefully control himself, presumably so he doesn’t bite Bella, and he knows that if Bella’s father knows about their relationship then there will be consequences for anything bad that he might do. Edward wants to be as constrained as possible—and doesn’t trust his own willpower to be enough—in order to protect Bella from himself.