Slavery was legal in the United States. Why would they need to secede to "preserve" it? Indeed it lasted longer in the Union than it did in the Confederacy. It took the Union another six months after the war to end legal slavery in the Union.
Lincoln fought the South to maintain the Union
To maintain economic control of revenue producing states in the South that produced nearly 75% of all Federal revenues prior to the War. It was about money.
Because the South believed that more Free States were going to be admitted to the Union and that would result in there being enough States so that an abolition amendment could be adopted without any Slave State ratifying.
As for the economic argument, slavery was key to the antebellum South's economy. To abolish slavery was to collapse the Southern economy. So when it came to the antebellum South, the economy and slavery were fundamentally linked. Also, remember the Southern States cited slavery as their principal reason for seceding.