Well, have some direct quotes from the people you mentioned.
Mississippi Secession Document (January, 1861): "That they have elected a majority of electors for President and Vice-President on the ground that there exists an irreconcilable conflict between the two sections of the Confederacy in reference to their respective systems of labor and in pursuance of their hostility to us and our institutions, thus declaring to the civilized world that the powers of this government are to be used for the dishonor and overthrow of the Southern section of this great Confederacy.”
South Carolina Secession Decree (December, 1860) “In the present case, the fact is established with certainty. We assert that fourteen of the states have deliberately refused for years past to fulfill their constitutional obligations, and we refer to their own statutes for the proof.
“We affirm that these ends for which this government was instituted have been defeated, and the government itself has been destructive of them by the action of the nonslaveholding states. Those states have assumed the right of deciding upon the propriety of our domestic institutions; and have denied the rights of property established in fifteen of the states and recognized by the Constitution.”
Virginia Secession Document (April, 1861): “The people of Virginia, in their ratification of the constitution of the United States of America, having declared that the powers granted under the said constitution were derived from the people of the United States, and might be resumed whensoever the same should be perverted to their injury and oppression; and the federal government having perverted said powers, not only to the injury of the people of Virginia, but to the oppression of the southern, slaveholding states.”
Alexander Stephens, “Cornerstone Speech”, (March, 1861): “Allow me briefly to allude to some of these improvements. The question of building up class interests, or fostering one branch of industry to the prejudice of another under the exercise of the revenue power, which gave us so much trouble under the old constitution, is put at rest forever under the new. We allow the imposition of no duty with a view of giving advantage to one class of persons, in any trade or business, over those of another. All, under our system, stand upon the same broad principles of perfect equality. Honest labor and enterprise are left free and unrestricted in whatever pursuit they may be engaged. This old thorn of the tariff, which was the cause of so much irritation in the old body politic, is removed forever from the new.”
Mississippi Secession Document, 1861 -
In the momentous step which our State has taken of dissolving its connection with the government of which we so long formed a part, it is but just that we should declare the prominent reasons which have induced our course.
Our position is thoroughly identified with the institution of slavery-- the greatest material interest of the world. Its labor supplies the product which constitutes by far the largest and most important portions of commerce of the earth...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."
The Declaration of Secession for South Carolina mentions slavery or slaves 18 times. No other cause is mentioned.
Alexander Stephens' cornerstone speech:
But not to be tedious in enumerating the numerous changes for the better, allow me to allude to one other -- though last, not least. The new constitution has put at rest, forever, all the agitating questions relating to our peculiar institution -- African slavery as it exists amongst us -- the proper status of the negro in our form of civilization. This was the immediate cause of the late rupture and present revolution. Jefferson in his forecast, had anticipated this, as the "rock upon which the old Union would split." He was right. What was conjecture with him, is now a realized fact. But whether he fully comprehended the great truth upon which that rock stood and stands, may be doubted. The prevailing ideas entertained by him and most of the leading statesmen at the time of the formation of the old constitution, were that the enslavement of the African was in violation of the laws of nature; that it was wrong in principle, socially, morally, and politically. It was an evil they knew not well how to deal with, but the general opinion of the men of that day was that, somehow or other in the order of Providence, the institution would be evanescent and pass away. This idea, though not incorporated in the constitution, was the prevailing idea at that time. The constitution, it is true, secured every essential guarantee to the institution while it should last, and hence no argument can be justly urged against the constitutional guarantees thus secured, because of the common sentiment of the day. Those ideas, however, were fundamentally wrong. They rested upon the assumption of the equality of races. This was an error. It was a sandy foundation, and the government built upon it fell when the "storm came and the wind blew."
Our new government is founded upon exactly the opposite idea; its foundations are laid, its corner- stone rests upon the great truth, that the negro is not equal to the white man; that slavery -- subordination to the superior race -- is his natural and normal condition. [Applause.] This, our new government, is the first, in the history of the world, based upon this great physical, philosophical, and moral truth.
So what were they fighting for, Pea?