The Confederacy did indeed secede on the issue of states' rights; namely, their states' right to permit people to own slaves without worrying about federally-imposed manumission/abolition or any other kind of interference in their "peculiar institution". They didn't really care about states' rights elsewhere, though, including demanding that the Fugitive Slaves Act ignore state and municipal laws and at one point demanding censorship in the mails to prevent abolitionist literature from being sent to the South. For several years they even enabled the forbidding of any petitions from the citizenry to the House of Representatives (an important aspect of common citizen involvement in the government in the era) on the issue of slavery, the infamous gag rule that was overturned on 3 December 1844 after years of campaigning against it led by Rep. John Quincy Adams (Whig-MA), former President (and the fellow who defended the Amistad
mutineers in the Supreme Court in 1840 - his argument to the Court was one big epic criticism and brutal putdown of the Van Buren Administration's craven behavior toward Spain).
Anyway, the Confederacy's advocates and defenders play the "states' rights" card a lot (and they love to play up the tariff issue too), but the fact is that any analysis of the actions, words, and behavior of Southern leaders shows that they did so for the explicit purpose of protecting slavery as an institution and that their actions were a petulant response to the Northern electorate ensuring Lincoln prevailed.
If you really want to rile up the apologists, you can adapt my term for the war.
When considering the South's record in the politics of America from the 1830s onward, and how they started the Civil War, I like to take the "War of Northern Aggression" crap and throw it back into their face: I call the ACW the War of Southern