In New York can a 17-year-old move out if they are being emotional abused by their parents?

Not legally. The law does not recognize emotional abuse as being grounds for a minor to be removed from parental custody unless such abuse has been documented by the state social service agency which has jurisdiction and is deemed to be a serious detriment to the minor's well-being. Minors who believe themselves to be in an abusive environment can call the National Child Abuse and Neglect Hotline, toll free, 24/7 at 1-800-422-4453 or 1-800-252-2873 for assistance.