The South perceived the Wilmot Proviso in this way because it would have confined slavery to the places where it already existed. This would have doomed the slave states to permanent minority status in the growing Union.
If the Wilmot Proviso had passed, the number of states with slavery would have remained constant. No new slave states could have been carved out of the eventual Mexican Cession. As the country grew, this would mean that free states would come to outnumber slave states by a wide margin. This would have allowed the free states to dominate the slave states. Therefore, the proviso seemed dangerous to the South.