How did the bank war and tariff controversy contribute to sectionalism and debate over the states' rights?

As the South found it increasingly hard to get new territories admitted to the Union as slave-states, they were increasingly outvoted in Congress.

This enabled the industrialised North to protect its manufacturing sector by raising tariffs on imports. The South, having almost no manufacturing industry, needed imports much more than the North did.

So the tariffs looked embarrassingly like the North directly taxing the South.

That is why South Carolina refused the pay the tariffs, claiming States' Rights - the right of one state to over-rule Federal law.