As the events at Ft. Sumpter show, the south had no intention of "peacefully withdrawing." Indeed, it was probably never in the cards -- Henry Clay's compromises (1820, 1833, 1850) were all about avoiding a civil war.
At any rate, they expected a fight, prepared for a fight, picked a fight, got a fight, and lost it. The concept of "peaceful secession" was never in play.
If the concept of peaceful secession was "never in play" it was because Lincoln said he would never allow it in the first place. The South prepared for a fight because Lincoln said he was going to bring them one. This despite the fact that the Constitution does not prohibit the States from secession nor does it grant the Fed govt the power to prohibit it. Still, you have not answered the question of why peaceful secession would constitute "insurrection" when nothing in the Constitution prohibits it and the Constitution specifically reserves for the States all powers not specifically delegated to the Fed?
Horse puckey. The events at Ft. Sumpter actually showed that both the state of South Carolina, and the Confederacy, were not in full control of their local militias, which understandably were not happy about a foreign military presense in their harbor, one that refused to leave when asked. Why would the Confederacy *want* to go to war with the Union, if secession could be done peacefully? They knew they stood little chance of beating the Northern Armies, since many of the leaders had at one time or another been officers in the Army. Once the shooting started, they knew the only chance they had to preserve the Confederacy was to win big early, and then negotiate an end to the war, perhaps with help from the British and French, and they almost pulled it off.