On November 10, 1860, South Carolina had an assembly to decide to secede or not which was called "Convention of the People of South Carolina". They decided to secede and on December 20, 1860, the seceded and declared independence. After this act, many more slave states decided to join them in the CSA.
Northern Perspective: The North was angry because they wanted the United States to be united rather than separate. Following the secession of South Carolina, many more southern states joined creating the CSA, who would fight the USA in the civil war.
Southern Perspective: The South supported secession for many reasons. The main reason they seceded was due to preserving the institution of slavery. They found the north as a threat to slavery and slavery is what their economy depended on. Without slavery, the south would be nothing and useless.