They had fired on the Star of the West and the Rhoda Shannon.
The Southerners were concerned only with the possibility -- the probability (about which they guessed aright) that Lincoln had been lying to them and would attempt to reinforce the garrison with more troops. He did.
It didn't have to happen. Lincoln's intentions to reinforce only if the resupply effort was opposed was made cleart to Governor Pickens and Major Anderson.
Starting a war was Lincoln's idea. I think he wanted a war all along --ever since 1856, when he finally concluded that there was no constitutional way to abolish slavery. (So, he decided on an unconstitutional one -- a civil war.)
Overcharacterization for polemical effect -- you do it well yourself. Ending slavery was never an overriding goal of the Union. Preserving it was an overriding goal of the confederacy.