https://psychcentral.com/blog/knotted/2018/02/the-lasting-pain-of-the-scapegoated-child#1
"The author of one study on scapegoating observed that having someone designated to take the blame allows a parent to paint much rosier picture of the familys dynamic since, presumably, life would be just grand if it werent for that pesky troublemaker. Needless to say, having a scapegoat around also makes it possible for the parent not to take responsibility for how the family functions. For the parent high in narcissistic or controlling traits, this is a win-win situation."