How we cite our quotes:
[Edward to Bella:] "To me, it was like you were some kind of demon, summoned straight from my own personal hell to ruin me. The fragrance coming off your skin...I thought it would make me deranged that first day. In that one hour, I thought of a hundred different ways to lure you from the room with me, to get you alone. And I fought them each back, thinking of my family, what I could do to them…" (13.103)
Edward talks of the danger he put his family in, as well as the guilt he currently feels for putting them at risk. Again, we realize that Edward's decisions aren't only about him, they impact the whole Cullen family.
[Edward to Bella:] "Alice and Jasper are two very rare creatures. They both developed a conscience, as we refer to it, with no outside guidance. Jasper belonged to another…family, a very different kind of family." (14.28)
Not all vampire families are like the Cullens. Notice how Edward pauses before saying "family." It's as if "family" isn't quite the right word for most vampire groups. This distinguishes the Cullens who truly do seem to love each other as a family.
[Edward to Bella:] "No, not many. But most won't settle in any once place. Only those like us, who've given up hunting you people" – a sly glance in my direction – "can live together with humans for any length of time. We've only found one other family like ours, in a small village in Alaska. We lived together for a time, but there were so many of us that we became too noticeable. Those of us who live…differently tend to band together." (14.35)
Edward's family is indeed rare. Not only do they not eat people, but also they can have a semi-permanent home, since they aren't, you know, killing their neighbors. This comment also implies that vampire families are, in part, bound together by their diets and morals, rather than by being biologically related.