Georgia did not give any general theory in favor of secession on general principle, but identified specific grievances against the North. In terms of Constitutional grievances, there were basically three:
- The Constitution did not give states any power to exclude slavery from the territories, yet they had been doing it since the Missouri Compromise in 1820, and the Republican Party was dedicated to preventing any further expansion of slavery whatever.*
- States were required under the Constitution (Article IV, Section 2, although the Declaration did not say so) to extradite criminal fugitives from other states, yet the Northern states did not extradite their abolitionists.
- The same article required the extradition of fugitive slaves, and the North did not comply with that provision either.
Nothing in the Declaration indicated that the Constitution authorized states to secede, let alone that it authorized individuals to engage in armed resistance.
Mississippi does not mention the Constitution at all,except to say that hostility to slavery predates the Constitution and can be found in the Northwest Ordinance. It then lists all the various ways Northern states have shown their hostility to slavery, up to and including electing a Republican President. "There was no choice left us but submission to the mandates of abolition, or a dissolution of the Union, whose principles had been subverted to work out our ruin." And furthermore, "Utter subjugation awaits us in the Union, if we should consent longer to remain in it. It is not a matter of choice, but of necessity. We must either submit to degradation, and to the loss of property worth four billions of money, or we must secede from the Union framed by our fathers, to secure this as well as every other species of property. For far less cause than this, our fathers separated from the Crown of England." Nothing in this Declaration suggests that the Constitution allows either secession or armed rebellion.
South Carolina was quite a different matter and was at some pains to argue that secession was constitutional. It began with a statement that the federal government had violated the constitutional limits of its power. It then went back to the American revolution. The Declaration of Independence declared the colonies to be "FREE AND INDEPENDENT STATES; and that, as free and independent States, they have full power to levy war, conclude peace, contract alliances, establish commerce, and to do all other acts and things which independent States may of right do." The Articles of Confederation provided "that each State retains its sovereignty, freedom and independence, and every power, jurisdiction and right which is not, by this Confederation, expressly delegated to the United States in Congress assembled." The treaty of independence recognized each state by name as "free, sovereign, and independent states." It emphasized the Constitution as "Articles of Union" that all states were free to adopt or reject and as creating a federal government as their "agent." It also emphasized the limited powers of the federal government and maintained that the Constitution is a "compact," i.e., a contract that all parties are free to withdraw from if the other parties do not keep the bargain. Unlike Georgia and Mississippi, South Carolina did cite specific clauses of the Constitution as having been broken, i.e., the criminal extradition clause and the Fugitive Slave Clause. But nowhere does the South Carolina Declaration cite the Second Amendment, either directly, or by saying that the right to keep and bear arms implies a right of armed rebellion.
Texas differs from the other states in that it really was (uncontroversially) an independent republic that voluntarily surrendered its independence to join the United States. As a result, Texas appealed less to any possible constitutional right of secession than its history as an independent republic that voluntarily joined the US and should therefore be free to go.
Florida did not publish a formal Declaration of Session, but did prepare one that was not published. Its only reference to the Constitution is to complaint that Northern states are not meeting their constitutional obligations under the Fugitive Slave Clause and that they are sorry to withdraw from any Northern brethren who have kept their constitutional obligations.
So, in short, of eleven states that seceded, four published formal declarations giving the reasons for their secession, and Florida had an unpublished declaration. Of all of these, only South Carolina made a serious argument that secession was constitutional, and none referred to the Second Amendment, the right to keep and bear arms, or a constitutional right of armed revolution. I do not intend to explore in great detail other Confederate defenses of secession as constitutional, other than that I have read some, and most follow the essential reasoning of the South Carolina Declaration -- that the Federal Union is a voluntary association of states that anyone may withdraw from at will. If anyone claimed to be exercising Second Amendment rights, I certainly am not aware of it. More to the point, if there had been any such claim, someone the Second Amendment movement would undoubtedly have cited it. That there has not been such a citation I take as proof that none exists.
*There was the awkward business of the Northwest Ordinance, which forbade slavery north of the Ohio and was adopted by the very first Congress under the Constitution. It spawned a veritable cottage industry attempting to explain it away.