The South left because of slavery and no other issue. They called it "States Rights" but the one right they were interested in was slavery. There is absolutely no reasonable debate whatsoever that the south would not have left the union and the civil war would not have happened if slavery did not exist.

Also, there was a legal argument at the time (explained by Lincoln himself as well as Seward and Chase - the most prominent republicans and whigs in the country) many years before the civil war that slaves were men and as such could not be owned as property and that their rights trumped the rights of States.