Why would citizens be the authors of society’s laws according to rousseau

Government was formed by the people, and they are the ones who will live under the laws.  So they should be the ones making the laws.

Rousseau's famous book on government was titled, The Social Contract, published in 1762.  In that book, he used the term "the sovereign" to refer to the people of a country.  Typically the term "sovereign" was used to refer to some king or ruler above the people.  But Rousseau saw that the people were really their own sovereign, in control of their own governance.  Any prince or ruler should function as an agent of the people to carry out what the general will of the people has shown itself to be.  (The idea of "the general will" is also a key feature in Rousseau's political writing.)