How did the americans disagree over the role of the federal and state governments before and after the during the civil war?

From what I can remember, states' rights was a large factor contributing to the Civil War. With Lincoln becoming president and representing the North, the Southern states seceded, leading to a war. The state governments of the South argued that since the Constitution and federal government was created by the states, the federal government had no right to stop states from seceding. President Lincoln and other northerners disagreed and wanted to preserve the Union by stopping states from seceding.
After the war, I believe the South still disagreed on a strong federal government. They wanted to rule the area by themselves.

Southern states and their dependence on slavery and the cash crop cotton believed that the State should be able to make and follow its own rules that its governor determined. Though the major factor of The Civil War was slavery, southern states believed that the Union shouldn't be allowed to harbor and care for Fugitive slaves that escaped the plantations, causing  distrust and aggressive actions towards the others and potentially starting the war.