The argument to say the South [i.e. the Southern States] was right is דין חלוקה the law of dividing.
That is, if you have a courtyard that is owned by two people and it is big enough to divide [about 4 yards by 8 yards], then either one can say to the other, "Buy my portion, or I will buy yours". They are not forced to stay together.
However, you can also say that a political union is not the same thing as a business arrangement.
After all, let's say one is living under a king, and he decides he no longer is subject to that king. That is treason.
So we see that politics and business are separate subjects although related. See for example Danny Frederick's critique on Dr. Michael Huemer. [Dr. Huemer holds no government is legitimate.
Frederick shows the flaws in his arguments. There was a debate in NY with Dr Huemer and a law professor of NYU that basically brought out these same point.