We just take Lincoln at his word. If he says it's not about slavery, then it pretty much wasn't about slavery.
Obviously, if there are two sides, there can be two motives. For Lincoln, it appears to have been about preserving the Union. For the secessionists, it appears to have been about preserving slavery.
Do you take Southern leaders at their word?
"African slavery is the cornerstone of the industrial, social, and political fabric of the South; and whatever wars against it, wars against her very existence. Strike down the institution of African slavery and you reduce the South to depoulation and barbarism." - South Carolina Congressman Lawrence Keitt, 1860
"Our people have come to this on the question of slavery. I am willing, in that address to rest it upon that question. I think it is the great central point from which we are now proceeding, and I am not willing to divert the public attention from it." - Lawrence Keitt
"What did we go to war for, if not to protect our [slave] property?" - CSA senator from Virgina, Robert Hunter, 1865
"The South had always been solid for slavery and when the quarrel about it resulted in a conflict of arms, those who had approved the policy of disunion took the pro-slavery side. It was perfectly logical to fight for slavery, if it was right to own slaves." - John S. Mosby [Mosby's Memoirs, p. 20]
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. --Mississppi Declaration of the Causes of Secession
What was the reason that induced Georgia to take the step of secession? This reason may be summed up in one single proposition. It was a conviction, a deep conviction on the part of Georgia, that a separation from the North-was the only thing that could prevent the abolition of her slavery. -- Speech of Henry Benning to the Virginia Convention
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. - Alexander Stephens.