I'll just quote straight from the horse's mouth, then. This particular horse happens to be Alexander H. Stephens, vice president of the Confederacy:
"Slavery was without doubt the occasion of secession; out of it rose the breach of compact, for instance, on the part of several Northern States in refusing to comply with Constitutional obligations as to rendition of fugitives from service, a course betraying total disregard for all constitutional barriers and guarantees."
He wrote this in his memoirs in 1866, basically right after the war ended. The "rendition of fugitives from service" he mentions was referring to the
Fugitive Slave Act, which essentially required Northern states to return escaped slaves to their masters based on nothing more than someone's say so (i.e., all they had to do was say, "Hey, I recognize that guy! He's one of my employer's slaves!"). This ran completely roughshod over the Northern states' rights, by the way, since it removed from them the ability to determine if a claimed escaped slave actually was, and how to determine this. Now, while Article 4, Section 2 of the Constitution did require the return of escaped slaves, and the Northern states had attempted to circumvent this to varying degrees, it does not excuse trampling their rights, now does it?
Another bit of hypocrisy regarding the fugitive slave business is that the Southern states held nullification of federal law to be an explicit right of all the states (look up the Nullification Crisis for more on that subject), so if they were consistent with this, there should have been no complaint about the Northern states exercising their rights by not complying with the law!
The South also didn't think much of Lincoln or the Republican Party, and one of the other reasons they seceded can basically be boiled down to the fact the country elected a President they didn't like! See, for example, a portion of Georgia's Declaration of the Causes of Secession:
"A brief history of the rise, progress, and policy of anti-slavery and the political organization into whose hands the administration of the Federal Government has been committed will fully justify the pronounced verdict of the people of Georgia. The party of Lincoln, called the Republican party, under its present name and organization, is of recent origin. It is admitted to be an anti-slavery party. While it attracts to itself by its creed the scattered advocates of exploded political heresies, of condemned theories in political economy, the advocates of commercial restrictions, of protection, of special privileges, of waste and corruption in the administration of Government, anti-slavery is its mission and its purpose. By anti-slavery it is made a power in the state."