This is a really important point and you have been severely misinformed. The states that succeeded were not shy about why. My own home state, South Carolina, after an extensive legal argument that they're allowed to succeed, revealed the great violation of their rights was the refusal to return fugitive slaves.
http://avalon.law.yale.edu/19th_century/csa_scarsec.asp
Someone else already linked to Mississippi. https://news.ycombinator.com/item?id=18474740
Slavery, to slave holders, was a state's right. That's the right they fought for.
This is an especially pernicious lie. A very small percentage owned vast plantations with hundreds of slaves, but the deeper into the south you went the higher the percentage of slave owners. 32% of all households in the south owned slaves. 49% of all Mississippi households and 46% of all in South Carolina households owned slaves. A slave was an aspirational purchase in the south; for those households that did not own a slave it was more likely to be due to poverty than principles.
"only" 1 in 20 white southerners in the confederacy personally owned slaves on paper, but this is like making an org chart of the institution of slavery & only counting senior management.
if you look at the 1860 us census & expand the analysis to slave owning households of the confederacy, the rate was closer to 1 in 3.