I am happy to be able to continue the discussion on more friendly terms. But, in my opinion, and I emphasize that this is opinion, the seceding states believed that they had every right to secede, inasmuch as the spirit of liberty that supposedly underlay the foundation of the country would have been contradicted had they not enjoyed that right. They did not view their action as a "rebellion". The only way that Lincoln could have acted justly, in my view, would have been to permit them to secede peacefully in the first place. Carthage was a nation founded on an entirely different concept and can hardly be taken as a basis of comparison.
Although it is only a movie, there is a line in "Gettysburg" that completely captures the reason the "constitutional legitimacy" arugment for the South fails: Tom Berenger as Longstreet says "what we should have done is free the slaves FIRST, then secede." But that goes to the nub of it: the only purpose for secession was not "constitutional rights," or even "freedom," but "freedom to enslave," and there is no such freedom implied in the Constitution, in that the 1st, 2nd, and 5th Amendments ALL de facto prohibited slavery.
I admit that the Constitution contained some contradictions but the weight of everything else IN the Constitution is for human liberty, not slavery (qua property).
Further, perceived PRECISELY that the Constitution was no good without the Declaration, and that it was only "law" so long as it was "dedicated to the proposition" that "all men are created equal." Without that proposition, it was no law at all, merely contradictions. The Civil War was about whose interpretation of the Constitution was right---Calhoun's, who said that the property clause superceded the liberty clauses---or Lincoln, who said that all the liberty clauses DEFINED the property clause.
Thus, it was impossible for the South to "free the slaves first," because the war was not about rights, or the Constitution, but ABOUT THE SLAVES.