Here's an article posted today that helps to bring this into focus.
A couple of points from the article: For the Confederacy, the war was almost entirely about slavery. Even the issue of States' Rights was mostly about the rights of states to maintain slavery. According to the article, the state of South Carolina wasn't all that interested in the right of the State of New York to deny the right of transit, essentially prohibiting slave owners from bringing their slaves to the state when they came to visit.
But for the Union, slavery was NOT the primary issue. Secession, and maintaining the nation, was. As denuseri notes in her latest post, Lincoln specifically denied that he was going to try to end slavery.

As for Fort Sumter, it is true that historians recognize the bombardment as the official beginning of the war, but events at the time were very muddled and it's difficult to determine where the actual point of no return was crossed.

However, denuseri, one point in the article you quote was misleading. According to Wikipedia (among many other sources):
Union attempts to resupply and reinforce the garrison were repulsed on January 9, 1861 when the first shots of the war, fired by cadets from The Citadel, The Military College of South Carolina, prevented the steamer Star of the West, hired to transport troops and supplies to Fort Sumter, from completing the task.
So the first shots of the war occurred before Lincoln even took office, but were NOT fired by South Carolina troops.

But there is controversy there, too. The city of Pensacola, FL contends that the first shot occurred on January 8th, hours before the cadets fired on the Union supply ship. And that it was apparently a blank cartridge!