Why was there a Bill of Rights added to the US constitution?

Federalists argued that the Constitution did not need a Bill of Rights, because the people and the states kept any powers not given to the federal government. Anti-Federalists held that a Bill of Rights was necessary to safeguard individual liberty. So, they were added to guarantee individual liberty and those rights could not be taken away. They were also added so that everyone had the same equal rights and nobody was lesser than anyone.