The issue of nullification aroused sectional differences because it showed that the South felt that it was being abused by the North and it showed that the South was willing to talk about secession in order to get its way.
The South felt that the tariff was a law that helped the North at the expense of the South. They felt aggrieved that the North would pass such a law. That aroused sectional anger on their part.
The doctrine of nullification, along with the related threat of secession, made the North suspicious of the South. It came to feel that the South was willing to destroy the Union in order to get its way.
In this way, the issue of the tariff and nullification aroused sectional differences and resentment on both sides.