When a child is treated radically different than their siblings as you were, they may have been assigned the scapegoat role. The scapegoat is often a sensitive child who's hyper-aware of the dysfunction in the family and, therefore, is resented by one or both parents. The scapegoat is the truth-teller who threatens the image of the perfect family that the parents so desperately want to display to the world. Because the scapegoat sees and feels things differently than the other kids, they're often viewed as “the other” and get blamed for anything that goes wrong.
A scapegoated youngster may grow up feeling deep shame but not understanding why. They may feel that no matter what they accomplish they're never good enough. They realize deep-down that they will never get parental approval and accolades. As an adult, they ask themselves the very questions you're wondering: Why was I singled out for bad treatment? Why were the others loved and not me? Why don't I feel close to my siblings? Why do I struggle with feelings of unworthiness?
Scapegoating is a common technique used by narcissistic parents. A good therapist can help adults who were scapegoated as kids to understand how it affects their lives now. That new-found awareness can free them from their designated role and relieve them of their shame, guilt, and confusion.