"Their main purpose, as indicated by all their acts of hostility to slavery, is its final and total abolition. His party declare it; their acts prove it. He has declared it; I accept his declaration. The battle of the irrepressible conflict has hitherto been fought on his side alone. We demand service in this war. Surely no one will deny that the election of Lincoln is the indorsement of the policy of those who elected him, and an indorsement of his own opinions. The opinions of those who elected him are to be found in their solemn acts under oath - in their State governments, indorsed by their constituents. To them I have already referred. They are also to be found in the votes of his supporters in Congress - also indorsed by the party, by their return. Their opinions are to be found in the speeches of Seward, and Sumner, and Lovejoy, and their associates and confederates in the two Houses of Congress. Since the promotion of Mr. Lincoln's party, all of them speak with one voice, and speak trumpet-tongued their fixed purpose to outlaw four thousand millions of our property in the Territories, and to put it under the ban of the empire in the States where it exists. They declare their purpose to war against slavery until there shall not be a slave in America, and until the African is elevated to a social and political equality with the white man. Lincoln indorses them and their principles, and in his own speeches declares the conflict irrepressible and enduring, until slavery is everywhere abolished."
Robert Toombs speech to the Georgia Legislature, November 13, 1860, advocating secession.
No, there is no doubt what "right" Toombs and Georgia were willing to fight for.
Here’s a link to the various Ordinances of Secession.
http://www.civil-war.net/pages/ordinances_secession.asp
To the extent that the states went on record to state a particular grievance identifying the specific state’s right that was being abrogated, with one exception it was slavery. The one exception was Missouri, which claimed it had been invaded by a hostile federal army. Texas threw in some comment about not securing the southern border, but the chief complaint there was slavery.
To those who say that the Civil War was about “state’s rights” and not specifically about slavery, they should read what the state’s own legislators said about why they were committing acts of rebellion and insurrection.