Good question. Why not give peace a chance, so to speak? Why go to war over Sumter which posed no real threat, militarily or economically, to the confederacy? Why go against the warnings of your own secretary of state when he warned that attacking the fort would be fatal? Was Davis stupid, desperate or both?
The likely reason is that Davis needed a war, badly. He was president of a seven state confederacy with no chance of thriving in the shadow of the much larger North. He needed the other slaveholding states to get off the fence and into the fold. Specifically, he needed Virginia, with the largest population of any slave-holding state and an industrial base larger than the seven original confederate states combined. But he knew that they wouldn't come in unless forced to choose sides, and the only way to do that is by provoking the North into military action. Davis banked that if he could bring in the 8 remaining slave-holding states then he could fight and win a war against the remaining United States. As it turned out, he only got half the remaining states and he lost the war, independence, the whole nine yards. Lincoln didn't kill the confederacy, it committed suicide.
That sounds like a reasonable theory, but I've never read it expounded anywhere but here. Do you have a historian I could read on that? I have only Nicolay on the origins of the war, and unfortunately he is very partisan. I didn't see a reference in him to Davis's motive in deciding to take Fort Sumter (which Lincoln surely left out there as a troll; but that's another story).
That all said, what you say "sounds right". And if I'd been there, I'd have slapped the taste out of ol' Jeff Davis's mouth, to call him to his senses. Even at the towering risk of being called out under Code Duello.
There was another motive that I've seen mentioned: Jeff Davis reasoned, by analogy with the American Revolution, that he was going to need European recognition as a palladium. If Lincoln continued to hold forts in Charleston harbor, Davis's failure to clear the remaining Federal installations in the South would be a major impediment to European recognition of the Confederacy. Have you read that one?