Why would every state want its own government?I'm kind of confused because isn't the job of the governor the same as the president?
Fundamentally, you are correct in your assertion that the central authority figure for the nation is the President and the state version is the governor. As a nation, America has had a strong connection to the idea of states' rights. The original Constitution of the nation, the Articles of Confederation, was conceived as a "loose confederation of states" where the states were seen as the ultimate authority, to the point where the federal government lacked all power unless the states gave their consent. Part of the reason for this was due to the framers' absolute fear of a strong centralized government. This fear of national government helped to create the belief that with state governments' autonomy, a level of check against the federal government could be created. This was fostered through the practice of federalism, a principle that articulated that there were certain duties outlined to the federal government and certain duties outlined to the state governments with certain duties shared between both governments.
The job of the governor is more or less the same as the president except only for that particular state. In other words, both governor and president are chief executives, but the governor is only chief executive of his or her state while the President is chief executive of the whole country.
States want their own governments because they each have different ideas about how things should be run. For example, different states have different ideas about what kind of taxes they should have and how high those taxes should be.