Why did many Southerners believe that they were the victims of an antislavery conspiracy?
I think that first you have to realize that many people tend to feel that there is a conspiracy against them when things don't go their way. That is why, for example, the Tea Party thinks Obama is trying to make America become socialist and/or Muslim and why liberals thought that Bush was trying to turn the US into a theocracy or a country run by big business. Therefore, it is not that surprising that Southerners thought there was a conspiracy when they did not get their way.
This sort of thinking was spurred on whenever events seemed to go against them. For example, when the Wilmot Proviso was inserted into various bills around the time of the Mexican-American War, they thought that showed the government was against them. Or when Northerners resisted the Fugitive Slave Act, they felt the same. Finally, when an anti-slavery candidate (Lincoln) was elected, they felt that proved that the North was conspiring to end slavery forcibly.