This is something I've been wondering for a long time. Was their ultimate goal to become an independent state, or were they just fighting for states' rights and willing to rejoin the Union? It always struck me as strange that they would want independence, because most other Civil Wars are waged because people want a change in government. Could the Civil War have ended in a different way?
Yes.
The people who pushed for secession were not angling for a better position in the Union; they promised a future of independence for the slave states, and a new union where their right to slave property would be enshrined forever as the cornerstone of a Southern confederacy.
Once the shooting actually starts, the letters of Robert E. Lee provide pretty explicit succinct statements of the Confederate cause. When South Carolina wanted to retain some troops for its own defense under the State's authority in December 1861, Lee argued forcefully that they should be devoted to national service, under the leadership of officers appointed by the President and Confederate Congress, rather than elected by their men as was common practice.
"The Confederate States have now but one great object in view, the successful issue of war for their independence. Everything worth their possessing depends on that. Everything should yield to its accomplishment."
There was a substantial peace movement in the North as well; one wing was willing to accept the permanent separation of the Confederacy, while the other wanted to end the fighting and return to wayward southern states to the Union through negotiation, rather than force. Lee believed that if the 'friends of peace' had their way and got an armistice, the Northern war machine would grind to a halt, and wouldn't start up again.
"Nor do I think we should in this connection make nice distinctions between those who declare for peace unconditionally and those who advocate it as a means of restoring the Union however much we may prefer the former.
We should bear in mind that the friends of peace at the North must make concessions to the earnest desire that exists in the minds of their countrymen for a restoration of the Union, and that to hold out such a result as an inducement is essential to the success of their party.
Should the belief that peace will bring back the Union become general, the war would no longer be supported, and that after all is what we are interested in bringing about. When peace is proposed to us it will be time enough to discuss its terms, and it is not the part of prudence to spurn the proposition in advance, merely because those who wish to make it believe, or affect to believe, that it will result in bringing us back to the Union. We entertain no such apprehensions, nor doubt that the desire of our people for a distinct and independent national existence will prove as steadfast under the influence of peaceful measures as it has shown itself in the midst of war."
Before the war, there had even been a popular (not universal, not even a majority, but certainly public) belief that the North had become a separate race from the South, and the way the Union brought the war to the South's civilian population during the war reinforced this notion. The Yankee became a barbarian or even a demon as they brought fire to the homes and land of southerners. Southerners decided they would not yield to an enemy that did the kinds of things Sherman did.