Fort Sumter, with its powerful guns, could bombard any point in the city of Charleston. Now Union Major Anderson had been ordered to refuse surrender of the fort, and a fleet of Northern warships was on its way to Charleston harbor. Soon, the South Carolinians would or could be targeted by the cannon from both fort and the fleet simultaneously. They decided to act before the fleet arrived, and deal only with the fort. They than began bombardment of Fort Sumter, for their own protection.
Here are some quotes from various sources that back me up:
"Increasingly it became clear that any attempt to relieve these garrisons [Fort Sumter and Fort Pickens] would precipitate war. . . ." (John Hicks, The Federal Union, Third Edition, Cambridge, Massachusetts: Houghton Mifflin Company, 1957, p. 558)
"Although Lincoln did not confess his part in provoking the Civil War with the cynical honesty of a Bismarck, he did speak certain revealing words. He consoled the commander of the Fort Sumter relief expedition for that officer's failure: 'You and I both anticipated that the cause of the country would be advanced by making the attempt to provision Fort Sumter, even if it should fail, and it is no small consolation now to feel that our anticipation is justified by the result.' Shortly after the fall of the fort he was quoted by a close personal friend: 'The plan succeeded. They attacked Sumter--it fell, and thus, did more service than it otherwise could.' A few of his party friends congratulated him upon his masterful stroke. The New York Times believed that 'the attempt at reinforcement was a feint--that its object was to put upon the rebels the full and clear responsibility of commencing the war. . . .' Jefferson Davis, others exulted, 'ran blindly into the trap.'" (Francis Simkins, A History of the South, Third Edition, New York: Alfred A. Knopf, 1963, pp. 213, 215-216, emphasis added)
Quotes are from the website Southern Heritage 411.com.