All you have to do is read the Articles of Secession. They are very clear.
The pressing and motivating force for secession was the right to extend slavery to the western states. Lincoln had conceded to leave slavery untouched in the old south, allowing it to die a natural death, but would not countenance its extension into the new western states. The south saw that if it did not spread they would eventually be outvoted in congress and... it would then be eventually forced out of existence.
So the war was a war over the western states. And had the south seceded without a shot fired, war would eventually have broken out anyway as the north and south competed for western territories.
So, the north fought to preserve the union. The southern soldier fought for his state. And the southern elite fought in their own words to preserve and extend the slave economy, and to give southern culture its own national expression, and to extend both into the unclaimed western territories.
Best summary I’ve seen on Free Republic regarding this mess of an issue.