Why did Southerners (and sympathetic Northerners) see Lincoln as such a threat?
This was because they saw him as a "Black Republican." They believed that he was going to be bent on abolishing slavery. They did not believe that he simply wanted to keep slavery from spreading to new territories. Instead, they believed that he would try to abolish slavery even in the South where it already existed.
Another reason for this was the fact that Lincoln was not even on the ballot in 10 Southern states. That meant that he owed nothing whatsoever to the South in terms of his election. Southerners and their sympathizers believed that this would make him even less likely to treat them in any sort of a fair way.
These attitudes can be seen in the following quote from the link below:
Many white Southerners believed that Lincoln's election meant that a final Northern push to abolish slavery throughout the United States was just around the corner. Countless furious speeches and editorials reflected the Southern certainty that the "Yankees," as the Northerners were sometimes called, would soon begin the process of reshaping Southern society without regard for the feelings of its white citizenry.