According to Confucianism, the society will function well if everyone knows their assigned place and does not question it.
In a Confucian society, people are not equal, instead, there is a hierarchy:
ruler >subject,
father > son, (we can assume that they mean parents> children)
husband > wife,
elder > younger,
friend = friend - here people are equal with respect to each other.
So we see that filial piety is a way of ensuring that this relationship: father > son functions without a problem, and the Confucians believed that this is necessary for the proper function of the society.