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.