Further answers are always encouraged, but as you wait for one you might be interested in this section of our FAQ on the Civil War.

Of those answers, this series of posts by /u/Georgy_K_Zhukov is the most in-depth.

The short version is that there are two sovereign rights of the states which the slave states where keen on: 1) The absolute right to hold slaves in perpetuity themselves. 2) The right to suppress any antislavery movements or legislation that come out of the free states, generally through the force of the federal government. I've written about this from a few different angles before, so I'll take this chance to offer up my stuff as a companion to Zhukov's mega-post.

This is a high-level consideration of what state's rights theoretically means and the South's track record with it.

This discusses state's rights rhetoric during the Nullification Crisis, which is often cited as a case of "pure" state's rights unconnected with slavery despite being driven entirely by slavery. More on Nullification here.

This looks at the Confederate Constitution from a state's rights perspective, finding that in the ultimate moment the white Sough forged for itself an ironcland commitment to coercing slavery into states and territories should the need ever arise.

This has the usual quotations from the secessionists themselves on their motives.

Further questions are very much welcome. I just didn't want to retype it all again. :)