Why did the election of Abraham Lincoln, who had pledged not to interfere with slavery where it existed, lead the southern states to secede?

The South's major objection to Abraham Lincoln was that he
was a Republican, a party formed on the express platform of preventing the extension of
slavery into the territories. Lincoln's election meant to the South that the Republicans
were gaining ground, and slavery would eventually be eliminated in that
area.

The existence of slavery in the territories was a
major concern because it was commonly accepted that these areas would one day become
states. If enough anti-slavery states entered the Union, a constitutional amendment
ending slavery could be passed and the "peculiar institution" would be doomed. It was
for this reason that the South argued vehemently for the admission of Missouri as a
slave state earlier.

As for Lincoln's pledge, he was
sincere. Lincoln believed--correctly--that slavery was constitutionally protected. He
pledged not to interfere where it existed because he believed he did not have the right
to do so. In fact, Lincoln had supported publicly and in writing the Corwin
Amendment which would have protected slavery where it existed. The Amendment
had passed Congress, and Lincoln wrote to every state governor, including those in the
South, urging its adoption. He believed this would preserve the Union. The South's
objection was not that Lincoln would attempt to end slavery then and there; but that his
election marked the movement of the country down a slippery slope which could only end
with the eventual abolition of slavery by constitutional
amendment.