Their reasons, as explained in their Causes of Secession documents, were nearly all slavery related.
And none were in any way different in December 1860 from what they had been for many years before.
And yet those same conditions did not cause secession all those years -- until the election of more Republicans in November 1860 made the Deep South fear for slavery's future.
As for Declaration-of-Independence type complaints: if you read those Secession documents carefully, it all boils down to just one truly serious item:
the Federal Government had failed to vigorously enough enforce Fugitive Slave laws in Northern states.
So, for the secessionists, it was all about slavery.
It was really only about slavery.
But it was the Deep South states that cited that most often. Just thinking logically, how many slaves could possibly make it hundreds of miles to get across the Mason Dixon line or the Ohio river to a free state from say South Carolina, Georgia, Alabama or Mississippi?
I doubt one in ten thousand, if even that, could have passed through all of that slave territory to make it to freedom before being caught. But fugitive slaves was an the issues they cited in their declarations. It was total bull.
The only slave states that really had a run away slave issue (and they were minor on the scale of things) were Virginia and the other border states such as Maryland, Delaware, and especially Kentucky. Yet the border states other than Virginia stayed loyal to the Union, and Virginia ended up losing their only border with the Mason Dixon line because the people who actually lived in that area remained loyal to the Union.
The entire Fugitive Slave issues was total political theater. The only thing that mattered to the Slave Power was expansion of slavery to the territories and with Lincoln able to prevent that expansion, they chose war instead of the status quo.