the werewolves in Twilight
aren't real werewolves.

“Though the creatures think of themselves as werewolves, they are not. The more accurate name for them would be shape- shifters. The choice of a wolf form was purely chance. It could have been a bear or a hawk or a panther when the first change was made. These creatures truly have nothing to do with the Children of the Moon. They have merely inherited this skill from their fathers. It’s genetic—they do not continue their species by infecting others the way true werewolves do.”

Caius, Breaking Dawn, Chapter 37