Why do every country need a state and public law but we have the federal law

It is because of two reasons :
Firstly the government of a country cannot handle all the works of the country, hence it has to make different laws in different states
Secondly, issues like health and other are a state subject which cannot be controlled by the central government unless and until it is not a national emergency
I hope you got the answer

Read your textbook to answer that question