We often assume by default that people make rational decisions based on complete information. That's debatable in the case of southern secession, but let's accept that as a premise, and ask whether it allows any explanation of why the Confederacy seceded in 1861 rather than waiting until later. I'll argue that there were three rational reasons that could explain this decision not to wait.
The new Republican Party had just won its first presidential election, with a massive electoral vote majority of 180 out of 303. It's true that Lincoln won in only 53% of the states, which is far short of the 3/4 majority that would have been required to pass a constitutional amendment outlawing slavery. However, the slaveholding states were looking at a situation where the parties had defined themselves according to ideological lines with respect to slavery, and with this new line-up, they were likely to be locked out of the White House forever. The Republican Party had a majority in the House, and had shifted the balance of votes in the Senate to the point where the Democrats no longer controlled a majority. Slaveholders were looking at the prospect of political oblivion, forever. The West was rapidly growing (as symbolized by the election of Lincoln, from Illinois), so there was a demographic time bomb in place if the Union kept admitting free states.
The Republican Party was completely inimical to slaveholders' interests. Their slogan was "free labor, free land, free men," and their platform called for no further expansion of slavery.
So the southern slaveholders had no rational reason to wait around before taking action, because there was no real hope of regaining political power. This was the reason for their insistence on states' rights and nullification.
As a modern analogy, I'm an American who was shocked and dismayed by Trump's hijacking of the Republican Party and election as president. If I believed that the Trumpists had a demographic lock on power that was likely to last for generations, I would be extremely embittered and radicalized.
In addition to the political time bomb, there was also an economic time bomb. The North was rapidly industrializing and growing in population, and they had a well developed rail network that proved to be a huge advantage during the war. It's not obvious to me that the Southern slaveholding regime clearly understood this, but the premise here is that we're going to try to explain their decision against delay under the assumption that they were rational actors with complete information. Under that assumption, rebellion later would clearly be doomed if the North chose to fight it, while immediate rebellion would have a better chance.
No political equilibrium can hold without security of property and territory. The South had seen the Haitian Revolution, Turner's Rebellion, and, most recently, John Brown's raid on Harpers Ferry. The slaveholding elite that held political and economic power had a very real and justified fear of a slave revolt. Although the Republican Party formally expressed dispproval of Brown, he was hailed as a hero and a martyr by many in the North. Slaveholders saw their slaves as both property and a potential security threat, and it was becoming clear to them that they would not get a sympathetic ear for their complaints about the threat posed both by and to their property.