Slavery was a big part of it. The abolitionist movement was big in the north, they had successfully got state laws passed against slavery, and this spooked the southern Democrats (Dixiecrats). They wanted to take a hard line stance against the Abolitionist movement in Congress to prevent an amendment from being passed, but the issue was that the northern Democrats had a lot of constituents who were sympathetic to the Abolitionists, even if they weren't Abolitionist themselves, so they had to be mindful about their rhetoric if they wanted to get reelected. This soft, wishy-washy approach didn't appeal to the Dixiecrats at all, and so the result was a schism in the Democratic party.
The 1860 election was a circus that makes 2020 or 2016 look sane. Abraham Lincoln, from the still very new Republican Party, won the election with only 39% of the popular vote, because both the Dixiecrats and northern, moderate Democrats ran their own Democratic ticket, splitting the vote between them. Each blamed the other for allowing Lincoln to win, and Lincoln had strong Abolitionist ties (though he himself was not an out and out Abolitionist, it was pretty obvious which camp he favored). The Republican Party however was the party of the Abolitionist cause. It rallied around that issue. As far as the Dixiecrats were concerned, Lincoln's election was an Abolitionist in the White House. And what was worse: they'd managed it without a single southern state voting for him. In effect: the south was totally overruled by the north and had no ability to affect national politics any longer.
The Dixiecrats announced their Secession from the Union on April 12th, 1861, just a few months after Lincoln's inauguration.