This means that the performance of a single family member, especially the children, directly reflects the whole family image. And how other families perceive your own is really important to them. This naturally incentivizes family members with authority / power such as your parents to be more demanding and controlling of their children. Imagine if you're a parent and if your children scores bad in school, other families or friends that you have will call you stuff like:
"You're a bad parent", "Your child is stupid, that must mean that her mom is also stupid." and so on.
Also imagine that other families are constantly gossiping about you or shutting your family off from friend groups because of a single mistake your child makes.
This would naturally make the parents want to force their children to perform good. And this incentive naturally flows into obedience as well and makes the whole power dynamic of the family feel like an authoritarian.