secession was in reaction to slavery, the civil war was in reaction to secession.
From the perspective of the south, it was like a wife wanting a divorce over a disagreement, but then the husband getting violent and forcing her to stay.
so you have to separate the two issues if you want to understand the two perspectives.
Lincoln actually did a lot of fucked up shit during the civil war, and should (imo) be seen as a villain. He fought to keep the states united, without regard for slavery except as the wedge issue on which to rally the north.
He even says as as much:
"If there be those who would not save the Union, unless they could at the same time save slavery, I do not agree with them. If there be those who would not save the Union unless they could at the same time destroy slavery, I do not agree with them. My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone I would also do that. What I do about slavery, and the colored race, I do because I believe it helps to save the Union; and what I forbear, I forbear because I do not believe it would help to save the Union. I shall do less whenever I shall believe what I am doing hurts the cause, and I shall do more whenever I shall believe doing more will help the cause. I shall try to correct errors when shown to be errors; and I shall adopt new views so fast as they shall appear to be true views."
So the war was fought solely to prevent secession, and that is where you must judge the intention. Slavery is the catalyst for the secession, but the war is not about slavery.