South Carolina seceded for two main reasons. First, they did not trust what Lincoln said. Second, they felt that even if he were not an abolitionist he would govern only for the North, neglecting the South or even hurting it purposely.
We should not be surprised that people in South Carolina did not believe Lincoln. Even today, many Americans believe President Obama is lying when he says he was born in America and when he says he is Christian. The Southerners of the 1860s simply did not think Lincoln was telling the truth.
Furthermore, Lincoln’s election was something of a last straw for the South. Since they did not trust him, they had been talking of seceding if he were elected. Since he was so unpopular in the South, he did not campaign there and was not even on the ballot in 10 states. So, the South had not cast any votes for Lincoln, and the rest of the country elected him after the South said his election would cause them to secede. Little wonder that they thought he would govern only for the North and that the North was going to tyrannize the South.