You already know what a scapegoat is since you have said you know you were the family scapegoat...

I think people use others as scapegoats so that they don't have to face themselves as who they are as people. It is easier to blame another, weaker person (as you would have been then, as a child (?) than now... though even if you weren't a child, family can always have emotional holds over relatives). Then they don't have to face their own shortcomings and weaknesses. And of course, if they're blaming somebody else, and see them always making mistakes, then they can feel justified in always putting down that person...