Claiming that slavery needed to be "protected" from the Union is the distortion. Not only was slavery protected by the US Constitution in Article IV, section 2, so too did Lincoln and his allies attempt to pass a constitutional amendment protecting it even further.
You may have missed it, but slavery was legal in the Union, and would have continued to be legal indefinitely if no efforts to leave had been made.
Therefore, it wasn't about slavery, it was about leaving.
That’s not what the southern leaders said;
Isham Harris, Governor of Tennessee, January 7, 1861, (Messages of the Governors of Tennessee, p. 255); “The systematic, wanton, and long continued agitation of the slavery question, with the actual and threatened aggressions of the Northern States and a portion of their people, upon the well-defined constitutional rights of the Southern citizens; the rapid growth and increase, in all the elements of power, of a purely sectional party,...”
Henry M. Rector, Governor of Arkansas, March 2, 1861, Arkansas Secession Convention, p. 44 “The area of slavery must be extended correlative with its antagonism, or it will be put speedily in the ‘course of ultimate extinction.’....The extension of slavery is the vital point of the whole controversy between the North and the South...Amendments to the federal constitution are urged by some as a panacea for all the ills that beset us. That instrument is amply sufficient as it now stands, for the protection of Southern rights, if it was only enforced. The South wants practical evidence of good faith from the North, not mere paper agreements and compromises. They believe slavery a sin, we do not, and there lies the trouble.”
S. C. Posey, Lauderdale County, Alabama, speaking to the Alabama Secession Convention on Jan. 25, 1861: “Mr. President, the fierce strife we have had with the Northern States, which has led to the disruption of the Government, is a trumpet-tongued answer to this question. They have declared, by the election of Lincoln, “There shall be no more slave territory–no more slave States.” To this the Cotton States have responded by acts of secession and a Southern Confederacy; which is but a solemn declaration of these States, that they will not submit to the Northern idea of restricting slavery to its present limits, and confining it to the slave States.”
John Tyler Morgan, Dallas County, Alabama; also speaking to the Alabama Secession Convention on January 25, 1861: “The Ordinance of Secession rests, in a great measure, upon our assertion of a right to enslave the African race, or, what amounts to the same thing, to hold them in slavery.”
“To remain in this Black Republican Union. . . (North Carolina’s) position must be one of degradation and bankruptcy. . . .I have but a few years left to me, but so help me God, they shall be spent in the cause of the rights of the whole South.”
Weldon Edwards North Carolina secession convention
That was not at all how things were perceived in the Deep South. The expectation there was that Republican appointments and policies would weaken slavery and contract the area where slavery was legal. Slavery would be locked out of the territories. This would be a blow to Southern honor or pride or self-respect or ego. Slaveowners believed that freedom included the freedom to own slaves and that equality included the equal treatment of slave property and other property. A government that declared that slavery was morally wrong was not a government that they wanted over them, even if it promised not to abolish slavery in areas where it was already established.
But keeping slavery out of the territories would have more practical and material consequences. It would drive down the demand for slaves, the price of slaves, their resale value and the wealth of slaveowners. It would be a blow to Southern wealth and credit. There was also the fear (based on what had happened in Virginia) that plantation agriculture would exhaust the soil - another blow to the Southern economy. And with no outlet for the growing slave population, slaveowners in majority slave areas would come to feel ever more insecure, as the proportion of the population that was enslaved grew - all the more so as Southern Whites moved west to free territories and were lost to the pro-slavery cause. The idea that many in the North and in the South - in the anti-slavery and in the pro-slavery camp - had was that "locking" up or "imprisioning" slavery in the South would put it on the road to extinction. Southerners saw their region losing wealth and power if they stayed in the union. Outside the union, expansion westward and southward was still possible through war or purchase.
There were other things that Lincoln and the Republicans could do. They could allow abolitionist materials to circulate through the mails, something that had been restricted since 1836. Slavery could be abolished in the District of Columbia. A plan of voluntary compensated emancipation could be adopted which would induce some slaveowners to get rid of their slaves, further weakening the institution. In the eyes of secessionist leaders, slaveowners in the Border States and the Upper South would be tempted to sell their slaves to federal resettlement programs, and thus slavery would eventually contract and be confined to the Deep South states, on the way to extinction.
Lincoln could also appoint judges, prosecutors and federal marshals, who it was feared would not enforce the fugitive slave laws. Even if Lincoln and his appointees had wanted to enforce those laws, they would be up against a large part of Northern opinion, and they would either have to comply with it or lose support at the polls. Southerners already regarded the Northern states' Personal Liberty Laws as a violation of the Constitutional compact: and things could only get worse for them if Republicans controlled the federal government.
Lincoln not only appointed court and law enforcement personnel. He also appointed postmasters, customs officials and other government employees. Secessionists feared that Lincoln appointees would form the core of an anti-slavery Republican Party in the slave states that would challenge the rule of the slaveowners. Buchanan had used his appointment power to promote the Democratic Party and his own faction on the West Coast. The secessionists' perception was that Lincoln could do the same in the South. There were already Republicans and anti-slavery activists in Missouri and Kentucky, and it was feared that Delaware would soon enough abolish slavery. Northern Maryland and Northwestern Virginia were already evolving away from plantation slavery. Once again, the larger fear was that slavery would be abolished in the Border States and then in the Upper South, until it was restricted to the Deep South, where it would wither and die.
Was this a realistic fear? I don't know. But the fear was real. You can read more about it on my personal page. Nobody familiar with the bitter, envenomed politics of the 1850s would conclude that an offer of a constitutional amendment would quell Southern fears and reconcile slaveowners to a Republican president.
There was no guarantee that such an amendment would be ratified either. In the North, the amendment would have caused great controversy and a split in the Republican Party. In the Deep South, slaveowners had made it clear that they didn't trust the Republicans and didn't want any compromise that was acceptable to Republicans. The possibility of an "unamendable amendment" was also questionable.
The Corwin compromise left open the possibility that states could abolish slavery - and the possibility that a growing Republican Party south of the Mason-Dixon line would support such a policy. The Confederate Constitution forbade any state from abolishing slavery. If you were a slave owner, which approach would be more likely to make you feel that your claim to your human property was unassailable?
The amendment was a last wild attempt at breaking the momentum of secession and was directed at the more moderate Border and Upper South states, rather than those states where the decision to secede had already been made. Those seven states were already out the door. No offer Lincoln made was going to win them back. Therefore, rejection of the offer can't be turned into an argument that secession wasn't primarily about slavery.
Southern Democrats convinced themselves that a "Black Republican" victory would be disastrous and would be just cause for secession. Slavery was the reason for this, but the association between a Republican win and secession had been so well established that secession was going to happen, at least in the Deep South. There was much passion and unrealistic fear involved, but the idea that a Republican victory would have dangers for the proslavery cause - whatever Lincoln said or promised - wasn't wholly wrong. Republican and secessionist views about slavery were so much in conflict that the half-hearted compromise offered by Lincoln wasn't going to be enough to satisfy Southerners.