1. State vs. Federal Rights
South Carolina thought that there would be plans fostered by Radical Republicans to limit and eventually abolish slavery. Even though it was not a power explicitly awarded to the Federal government in the Constitution.
2. Social Differences
The North was economically different from the South. The Southern States did not believe that the federal government had their best interests in mind. One of these differences was the use of slaves on large plantations, but it's influence was minimal. A large part was the difference in industry, with the North's economy being largely based on manufacturing, and the South's on agriculture.
The election of President Abraham Lincoln, a Republican, was a huge factor in the decision by South Carolina to secede.