Other then the right to own slaves, what other States Rights was the South fighting for? The right to withdraw from the Union, I believe was one.
To look at this in futuristic terms:
Let's say a few years from now when the growing international economy has all but dissolved nationhood, the United Nations votes that all members should abolish the death penalty.
Then let's say America says to heck with that, I'm outta here.
Then the United Nations says, "You can't leave!" and begins assembling a blue-helmeted army to invade America.
What then would you be fighting for: the death penalty or the right to remain a sovereign state?
If you care to check you will find that NO founders believed in a unilateral right of withdrawal from the Union. Why don't you see what Madison said about it? And don't trot out the 10th amendment as an argument it had NOTHING to do with anything which would change the Union merely acknowledged States having the right to adopt their own judicial codes and regulations WITHIN their borders as long as they were consistent with the US constitution.
There is only ONE way to change the constitution- by amendment. A state could legally secede ONLY if an amendment were to be passed allowing it.