It’s usually “They seceded to protect states’ rights”, and “They seceded to protect states’ rights to secede” kind of runs into an issue when you consider that the Confederacy did not regard Confederate states as having the right to secede.
They seceded because they did not have faith in the union to enforce slavery, which was federal law. There were more government representatives from slave owning states, and there was no risk of abolition prior to their secession.