Lincoln didn't. The southern states did. The South seceded because the state right they were worried about losing was slavery. CSA Vice President Alexander Stephens put it best in his Cornerstone Address.

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...

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. This, our new government, is the first, in the history of the world, based upon this great physical, philosophical, and moral truth. This truth has been slow in the process of its development, like all other truths in the various departments of science. It has been so even amongst us. Many who hear me, perhaps, can recollect well, that this truth was not generally admitted, even within their day. The errors of the past generation still clung to many as late as twenty years ago. Those at the North, who still cling to these errors, with a zeal above knowledge, we justly denominate fanatics.

You're arguing that the CSA wasn't founded on slavery but one of it's founders is arguing the exact opposite. That slavery is literally the cornerstone of the new government.