I think Mississippi, South Carolina, Texas and perhaps Georgia said it was about slavery, but All the rest, (the other 7 states) did not.
It has become convenient though to represent the 3 or 4 that did, as speaking for all 11 states. This is done because people want to push this narrative to justify what was done to all the Southern states.
But regardless of their reasons for seceding, the fact remains that the Declaration of Independence asserts the right to do so, and if it was good enough for the 13 slave states that became the USA, it was good enough for the 11 slave states that became the CSA.
Yes they did.