In our government the people choose a leader (the president) and we are able to not have the same beliefs as others, and we are allowed to criticize the government. Whereas in the divine right god chooses who to rule, or someone rules claiming in the will of god. Basically if you were to criticize anything the ruler says you'd be testifying against god's word. Our government is a democracy and the divine right is more of a one person leadership kind of like a dictatorship per se.
