Yeah, the states' right to own slaves.
Ever wonder why, Mississippi for instance, explicitly stated this in their articles of secession?
“Our position is thoroughly identified with the institution of slavery — the greatest material interest of the world. Its labor supplies the product which constitutes by far the largest and most important portions of the commerce of the earth. . . . A blow at slavery is a blow at commerce and civilization.”---Mississippi in its own secession declaration, passed Jan. 9, 1861.
The South wasn't interested in state's rights unless it was to further their interests in maintaining slavery.
For instance, the southern states/the Confederate states opposed states’ rights — that is, the right of Northern states not to support slavery.
And remember, until the Civil War, Southern presidents and lawmakers had dominated the federal government.