The South seceded because they did not want the North to be able to tell them what to do. In specific, they did not want the North to be able to do anything that would hurt the institution of slavery. They feared that the North would do that once Abraham Lincoln became president.
Lincoln had been elected without getting any votes from Southern states. This made the South believe that he would govern only for the benefit of the North. As part of this fear, they were afraid that he would abolish slavery in the South.
The South wanted to be left alone to rule itself, which meant having slavery. They feared that Lincoln would not let them have slavery, so they seceded.