You're confusing cause and effect. The goal of the south was slavery and leave if they did not get it - cause. The north was then handed a problem to which civil war. Effect. The south lost. Lincoln was trying to avoid bloodshed by arguing that the union could not be recinded unless all agreed. As such he was arguing for a third way to resolve the issue. The south didn't find third way. It got the problem it wanted and paid the price for it.