Except, they didn't. If anybody thought even the original 7 seceding states' primary concern was the preservation of slavery, Lincoln and the Northern dominated Congress passed (with the necessary 2/3rds supermajority) the Corwin Amendment which would have enshrined slavery expressly in the constitution and made if effectively irrevocable. The original 7 seceding states turned down the offer of slavery forever in exchange for returning. The Upper South did not even choose to secede until Lincoln chose to start a war to impose federal government rule over people who no longer consented to it. Please do not try to revise history to argue otherwise.
All of the articles of secession mention slavery as a reason for seceding.