In the book Twilight new moon why did Edward leave Bella?
Edward believes if he stays away from her she will be safe since when she got a cut on her birthday, Jasper launched himself at her and he believed it was dangerous to Bella if they stayed in contact so he pretended to leave her so she would be protected.
edward feels that if he stays with bella then she will always be in harms way but if he leaves her then she will be much safer
Edward left Bella for her own safety. Not just by Edward's brother, Bella can be harmed by any other vampire, even Edward himself. Edward wants to see Bella happy and so he realized the huge risk in falling in love with a human being and thought it would be best for her if he left.
There is a scene in the book where Bella is nearly attacked by Edward's brother on her birthday in his house. The family endeavors to live as humans and so do not drink human blood. But after he senses Bella's blood near him, Edward's brother nearly loses control and attacks her. Edward feels it wise to leave Bella and keep her out of harm's way. Vampires are unpredictable and he wants to act in her best interest.