Lincoln's war wasn't about abolition. It was about unilateral secession and an attack on US troops at Ft. Sumter. Now secession, that was all about the fear that the Republicans would prevent the expansion of slavery into the western territories. You just have to read the Declarations of Causes that South Carolina, Georgia, Texas and Mississippi issued to see that's true. Not to mention a hundred other southern sources.
The Corwin Amendment was an attempt to show the south that Lincoln had no intention of interfering with slavery where it already existed. But for the south, that wasn't enough. So they took their marbles (and all the federal facilities in their states) and went home.
And just what were those federal troops at Ft. Sumter doing? (Hint: it didn't have anything to do with slavery, but it did have a lot to do with what motivated many southerners to support withdrawal from a union that was increasingly in the thrall of northern mercantilist interests.)