Rerunning an older post, revised a bit based on things I've learned since:

Lincoln was legitimately terrifying to the South on a few different levels, all of which come down to slavery. By 1860, the conviction had grown at least in the Lower South (the Cotton Kingdom, essentially the seven states which seceded before Lincoln was inaugurated) that it was completely unacceptable to entrust the federal government to an administration not comprised of and/or heavily beholden to slaveholders. Both of those had been the status quo for something really close to the entire history of the United States as an independent nation.

A non-southern president had never won re-election. All previous administrations, headed by a southerner or not, had southerners in positions of influence. Southerners and the party where southerners were more disproportionately influential (the Democracy) governed the nation for the lion's share of its history. Because the section was, at least nationally, far more unified than the North it's ability to shape governance is hard to overstate. It was so conspicuous even when a northerner was president that by the late antebellum antislavery Americans think there's a genuine conspiracy at work between southern politicians and willing collaborators in the North to advance slavery. This, per antislavery thought, had its root in the Slave Power. That was originally the extra representatives and electors that the South got thanks to the 3/5 Compromise. By the late antebellum, the Slave Power had grown beyond the original meaning to cover the disproportionate influence of the slaveholding section. It was literally power in slaves, but both the thing itself and the penumbra around.

Lincoln was elected without the support of a single Southern state. He wasn't even on the ballot in most of them. His party was avowedly sectional, confined to and deriving all its support from the North. As such, it had no reason to treat the South's interest in slavery with any deference. Nor did the electoral map as it was then developing appear to suggest that it would ever need to, as immigration had tilted the demographics very much in favor of the free states. He, and any future Republican administration, had no incentive to even appoint Southerners to high offices where they could moderate things.

That would be bad for the South in itself, but it gets worse. The GOP was not on the ballot in the South and got no votes there because it was functionally anti-Southern. I don't mean by this that they had a kind of racial hatred toward white southerners, but rather that the party's entire purpose was to defeat the South's single unifying issue, the very thing that made the South southern: slavery. Another necessary disclaimer applies here: I'm not saying that slavery is the only thing of any significance about the South or that it's the only thing southern whites thought about. But it was, they made very clear and generations of historians have agreed, the central fact of southern life and center of gravity for southern politics.

Let me reframe that just a little. Almost everywhere in the South (Missouri is a notable exception.) had at least a county or two where blacks heavily outnumbered whites. In the case of South Carolina and Mississippi, this is true of the whole state come '60. Louisiana is close to the tipping point. In most of the Lower South, there's are whole regions of the state like this. And even elsewhere, any enslaver with enough slaves to be conspicuous in the community has the day to day experience of being significantly outnumbered. All those slaves? Just about none of them are ever happy to be slaves. Keeping them slaves is a huge deal, because otherwise they're bound to get it in their heads that you just really need to be killed dead for all the things you've done.

Actual evidence of genocidal designs by American slaves is not zero, but it's close. There are slaves who confessed to revolts where the plan was to kill all the white people in town, but their confessions were frequently tortured out of them. And there were cases of slaves revolting and killing whites, albeit in usually quite small numbers. (The most famous of these, but not the largest, is Nat Turner's revolt.) These provoked wildly disproportionate massacres by whites. Any slave might be plotting something; you just had to be sure. If not on a grand scale, then your slave valet who might literally sleep in the same room with you might just decide one day to slit your throat or poison you. We know with hindsight that the fears were overblown, but they're not irrational.

Failing that, there's a whole lot of money invested in slavery. The only asset that beats the aggregate value of the nation's four million slaves was the land itself, from sea to sea. The South had more invested in slaves than the nation did in factories and railroads combined. Lincoln would aver in his second inaugural, "These slaves constituted a peculiar and powerful interest". They weren't just going to give it up and take the loss. Nor did the cash exist to compensate them all at fair market value, a fact noted as early as the 1830s. Though to be fair, the Southern political class was against compensated emancipation well before that.

So Lincoln's election means that the South has lost control of the federal government. Its central interest, the Southern interest is now at risk. And the Republicans were openly gunning for it. The full story of this is the political history of the United States at least 1848-1860 and arguably much further back. For immediate threads, here are some:

1. The Republican Party did not accept the Dred Scott decision in any of its famous particulars. They believed that the Congress had the power a ban on slavery in the western territories. Everywhere such a ban had previously been inaugurated, going all the way back to the Northwest Ordinance, it had resulted in free states. (This was a close call a few times and early Illinois and Indiana were not particularly free, but it had worked out that they became so.) If they did establish slavery bans by, say, reinstating the Missouri Compromise, then that walls off future expansion for American slavery. With the slave population growing and limited frontiers for new plantations, the reasonable fear was that slave prices would drop. That would provoke panic selling and everybody would be ruined.

2. This included filibustering. Freelance military expeditions to conquer points south of the border, most notably Cuba and Nicaragua but also parts of Mexico and other, less popular, locales with an eye to their subsequent annexation to the United States as slave states were controversial in the South. But it was a way to expand slavery in theoretically less fraught circumstances than fighting over already-acquired territory. Now and then Senators would even list off areas, shopping list style, as future slave states. The high tide of southern filibustering is arguably the early 1850s, but that's more clear in retrospect than it was then. The Republicans, like the Whigs before them, were not fond of this at all and were unlikely to either turn a blind eye or actively facilitate expeditions like previous administrations had done. (The Pierce administration is especially suspicious-looking on this front.) The GOP platform was no new slave states, period. Lincoln rejected a last-minute compromise proposal to reinstate the Missouri Compromise with an explicit institution of slavery south of the line, on the grounds that it would be a declaration of war on everywhere from Texas to Tierra Del Fuego.

3. The Republicans would say, especially as things got hot in 60-1, that they were willing to accept the Fugitive Slave Act of 1850. But plenty of prominent antislavery men who were now Republicans had protested and even actively fought enforcement of that law. (This resistance had cost some slave catchers their lives.) The free states had expressed their powerful, if often a little more rhetorical than factual, determination to thwart it. In the late '50s, Wisconsin actually nullified it. This was not necessarily a big issue for the Lower South, from which few slaves escaped, but was a bigger factor for the Border South (states adjoining on free states). However, the Lower South had largely signed on for the Georgia Platform after the Compromise of 1850. The short version of that is: "We do not like this compromise one bit, but we agree to remain in the Union on the condition that you stick to the Fugitive Slave Act." As such, denunciations of Northern faithlessness on this front, and in reference to personal liberty laws going back further, feature prominently in some of the Declarations of Causes for secession. In light of all of this, the GOP's promise to stick to the law (until repealed, anyway) can't have been very convincing.

(Continued in a moment.)

This has already been answered, and I'm not an expert historian.

My high-school history teacher had a saying that stuck with me. He said, "they had a boogeyman under the bed." In otherwords, they were paranoid over something non-existant.