In the past the abused child was often the step child and that is still true today. That is where the phrase "beat like a red headed step child" comes from. But once again there are exceptions and the child selected may be biologically the child of the parents and a full sibling to the rest.
It is a very weird sort of family dynamic and the parents usually maintain that they are doing nothing wrong that it is all the scapegoated child's fault. That they are difficult, rebellious, destructive or even insane and the parents are just trying to control them.
And there is the flip side. Sometimes out of several kids there is one who is "difficult, rebellious, destructive or even insane" and the parents are legitimately just trying to control them.
Probably not the case here through.
A lot of these stories seem to be about autistic kids. They are different from the others, can be difficult to control, and the parents just grow to hate them.