For what reasons did seven southern states secede from the Union shortly after Lincoln's election in 1860?

The
Southern states wrongly believed that Lincoln was planning to abolish slavery outright. In
actual fact, the Republican Party platform on which Lincoln was elected was merely opposed to
the spread of slavery. But to most Southerners, this was bad enough, and they genuinely feared
the worst. As slavery was the linchpin of Southern society and the Southern economy, a growing
consensus quickly emerged that the South should secede from the Union in order to protect its
way of life.

The Southern states justified their secession on the grounds of
protecting states' rights. But in actual fact, there was only one right they were seeking to
protect, and that was the right to maintain the institution of slavery. They felt that that
institution was under threat with the election of Lincoln, so they seceded and, in doing so,
precipitated the Civil War.