Firstly, the "average person" in the Antebellum South was probably not very politically involved or aware. They were probably even more influenced by "sound bytes" than we are today. It's very likely that the notion that "Lincoln wants to ban slavery" was as an adequate rallying point for people to get behind. However, it's important to look at these issues in the context of the times. The South was dominated by white landowners whose subsistence was dependent on the subjugation of others, slavery built and maintained their wealth. Even poor whites who were not slave owners had a vested interest in retaining the status quo, so that they were not the bottom rung of the socio-economic ladder.

Slavery had already been banned in many of the Northern states, and Lincoln and the Republicans had expressed a desire to contain slavery to the South. In 1860, The Republicans won the majority in the Legislature, and captured the executive with the election of Lincoln. This article makes a strong argument that secession was an overreaction to the Democrats losses in the election, and a fear that this election would directly lead to the continual erosion of their political capital.

This is a useful source for you that contains the actual documents issued by the seceding states.

Southern States argued that because all powers not explicitly stated in the Constitution are given to States and because secession was not a topic explicitly mentioned in the Constitution they were allowed to leave the Union as they had joined as sovereign entities. However Lincoln and northerners disagreed and insisted the states remain in the Union and left Federal troops in Fort Sumter until it was attacked oficially starting the war.