Okay so this song being in Twilight makes perfect sense, and it could be from either Bella or Edward's point of view, if you think about it. They both have to sacrifice something in order to love each other. But they are willing to do that, no matter how dangerous. This song being from Bella's point of view could be about how she is on to Edward, and realizes who/what he really is. She is smarter than he thinks, and she kind of wants him to know that. Now, on the other hand this song being from Edward's point of view for example "I won't soothe your pain" and "I got nothing for you to gain" "you'll be waiting in vain" he sees himself as a monster and warns Bella that falling in love with him is not a good idea. Remember his confession to her in the woods? It also makes sense that this song is in the first movie, cause a lot of the lyrics make sense to be in a movie where the other person is still finding out who the other truly is and wants them to know they won't be fooled by them, and that they have their own power.