I'm sure someone can give you a better answer to this but I think it depended a lot on when you are asking, and what member of the Confederacy you are talking about - it is important to remember there is considerable variation among the founders of the Confederacy. The early advocates for secession like Robert Rhett, and Robert Toombs went to considerable efforts to tie themselves to the founders. The Confederate administration was initially pretty sympathetic to this rhetoric. Jefferson Davis said as much in his first inaugural, “It is by abuse of language that [the Confederacy’s] act has been denominated a revolution...we have changed the constituent parts, but not the system of our Government. The Constitution formed by our fathers is that of these Confederate States.”

However as early as Alexander Stephen's (the Vice President of the Confederacy) Cornerstone Address there seems to be a move away from the founders: “the prevailing ideas [among the founders was that slavery]…was wrong…it was an evil…those ideas were fundamentally wrong. They rested upon the equality of the races.” And, “our new Government is founded upon exactly the opposite ideas [of the founders]…its cornerstone rests, upon the great truth that the negro is not equal to the white man…slavery…is his natural and moral condition…our new Government, is the first…[to be] based upon this…. truth.”

I don't think any of this amounted to a complete rejection of the founders, e.g. Washington and Jefferson who I believe remained revered in many respects, but there was a clear belief that they had erred in writing the Constitution and particularly in the Declaration of Independence.

Hope this helps, I'm sure someone can elucidate this further.

There is a reason that the American Civil War is sometimes labelled the Second American Revolution. And while none of what's stated below contradicts the conclusion that slavery was at the heart of the war's causes, it's important to remember how that process took shape. It was not simply "if slavery==good, return Confederacy" and "if slavery==bad, return Union," but rather how slavery affected a wide range of political, social, economic, and legal disputes which ultimately dissolved into war. And interpreting the Constitution and the Founding generation which crafted it played a large role in the rhetoric of both sides, so this is actually a fascinating question about an easily overlooked facet of the war's causes.

It is not a coincidence that the Civil War took place within a decade or two of the final disappearance of the revolutionary generation. Once not only the Founding Fathers, but all Americans who had personally witnessed the revolution passed away, the ideas and legacy of the nation's origin became an unequivocal matter of interpretation. No one was alive to say "what had happened" (accurate or not), so the matter was entirely in the hands of those who had never experienced it. What is the proper interpretation of the Constitution? What are primary American values? What did the Founders mean when they said nebulous words like "freedom" and "liberty"?

It didn't help that the Constitution was itself ratified ambiguously. If you read the Federalist Papers you'll find arguments for state authority and for federal supremacy. Southern states were promised that the Constitution's ambiguous statements on slavery would protect the institution while Northern states were promised the opposite. So when we fast forward to the antebellum period and see political battles raging over slavery and the Constitution, we see Southerners able to call upon their own version of events, the intentions of the Founders, and interpretations of the Constitution while the North can do the same.

So, in retrospect, which side was "right" in their interpretation? Was slavery protected or not by the Constitution? Did the Founders want it to endure, or wither? The best answer historians have been able to churn out amounts to, basically, "I dunno." If we set the immorality of slavery aside for a moment, as well as any personal feelings we might have each side of the conflict, it's clear that both supporters and opponents of slavery were able to make pretty damn solid, evidenced arguments for their viewpoint, and the ambiguities of the Founders (who were a diverse group with diverse opinions), the Constitution, and its ratification process were enough to keep one side from effectively shutting down the other. One compelling historical argument I've heard is that the ultimate constitutionality of slavery was decided not in the courtroom but on the battlefield (Texas v. White having taken place after the fact).

So with that, on to your specific question: Confederate leaders, by and large, felt that in seceding they were largely remaining true to what they believed to be the true legacy of the Revolution. They were preserving the Constitution as it was meant to be by rejecting a Northern administration which they were convinced would destroy it. They equated secession to the rebellion of the Founders themselves and felt they were honoring that revolutionary spirit and legacy. And they believed they a strong institution of slavery was an integral part of that vision.

Given how American history had played out to that point, their conclusions were not irrational or completely erroneous. Please bear in mind, hypothetical Lost Causer who reads this, that this in NO WAY automatically validates the Confederate cause, viewpoint, interpretation of the Constitution, or anything else they believed in. What it does indicate is that the meaning of this thing called the United States is not a static value but rather a constantly renegotiated process that has historically had the power to shape the development of vast cultures and geographic regions, at times violently.