In the novel "Twilight," why is Bella afraid to meet Edward`s family?

In "Twilight," Edward and Bella have been dating for quite a while when Edward finally suggests that it is time for Bella to meet his parents.  At first she gasps, and Edward asks if she is afraid, and she replies that she is, but she goes on to explain,

"I'm not afraid of them," I explained. "I'm afraid they won't... like me. Won't they be, well, surprised that you would bring someone... like me... home to meet them? Do they know that
I know about them?"

"Oh, they already know everything. They'd taken bets yesterday, you know" ­ he smiled, but his voice was harsh,­ "on whether I'd bring you back, though why anyone would bet against Alice, I can't imagine. At any rate, we don't have secrets in the family. It's not really feasible, what with my mind reading and Alice seeing the future and all that."