to leave the Union.
I am going to do what I can to analyze the South's rights under the common legal thought of the time and that is natural law/natural rights.
To begin the analysis, the South's stated reason for leaving the Union was state's rights. However, what right were they protecting? Slavery. The essential question, then, is whether or not slavery is something that should be allowed under a natural law theory.
I think we can, rightfully, conclude that slavery is not a natural institution and certainly not allowed under a natural law theory. Slavery is wholly unnatural and was a "hideous blot" and should have never been instituted and it violates all of God's laws. This means that no one has any "right" to own slaves.
The question now becomes, can a member of the Union leave the Union to protect their ownership interest (for I cannot call it a right) in slaves even when such interest is not a right? Again, the answer is negative. That is not a proper justification to leave the Union, elsewise we would not have a Union in truth.
Under the then prevailing legal thinking, the South had no right to leave the Union. The war they started was not justified on their end, but was justified on the part of the North.