The argument from the perspective of a secessionist was similar to the argument for independence from Great Britain. The American Revolution was based on the fact that Britain did not respect the Colonies and they demanded that the American Colonies paid taxes even without any representation in the British Parliament.
The secessionist argument was a little different because the Southern States had representation on Congress but they defended that even so the Union disrespected the States rights and liberty of deciding if they would accept Slavery or not.
In the end, both arguments laid on the fact that they believed that their rights were being stripped away and that they should break that dependent relationship so they could gain those rights back.