Why did the South think that the election of Lincoln in 1860 meant that their lives would be different?

When he got the nomination from the anti-slavery Republican Party in 1860, the South was very concerned. The South had made up its mind. They believed Lincoln would end slavery. However, if they would have listened closely to Lincoln, he had said if he could keep the country together by keeping slavery, he would do so.
And

For the most part, states in the South reacted with anger to Lincoln's victory in the election of 1860. The major issue of the 1860 presidential election was slavery. For Southerners, expanding slavery was the critical issue. Slavery was so pressing that the Democratic party put forth two candidates.