The Tariff of 1857 was passed by the Southern-dominated Buchanan administration after the Election of 1856. It was the lowest tariff yet, exactly as low as "the South" had wanted (as the Fire-Eater leader Rhett knew and admitted in December of 1860 at the South Carolina Secession Convention). The Tariff of 1857 was the brainchild of Senator R. M. T. ("Run Mad Tom") Hunter of Virginia.
Unfortunately, the Buchanan Administration presided over an economic disaster. They arrived in office with a pile of money in the Treasury, an annual budget surplus, and a declining National Debt. They didn't think the government should have money, so they spent the cash. The new Tariff of 1857 went into effect just as the boom of the 1850s went bust. Between the lower rates and the Panic of 1857, government revenue declined while the Buchanan Administration spending increased. The budget surplus turned into a huge budget deficit. The National Debt mushroomed. Banks began demanding higher interest rates on government loans. To top this all off, a major embezzlement scandal involving Secretary of War John B. Floyd and funds from the War Department and stolen bonds from the Treasury Department was hitting the light of day in late 1860.
That was when the 1st Morrill Tariff was proposed and passed the House in 1860; Senator Hunter blocked it in the Senate, making it an Election issue for 1860. "The North" (as in "the rest of the country") generally felt the Tariff of 1857 was too low and was allowing US industries to be hurt (particularly iron and steel). "The South" was opposed to any increase at all from the historially low rates of the Tariff of 1857. They made no effort to propose any way at all to deal with the booming National Debt, the large budget deficit or the empty Treasury. Essentially, they were for "the South" ahead of the Country.
That, in a nutshell, is what the Tariff issue in secession is: one section putting their own desire above the interests of the country as a whole and refusing to compromise with the rest of the country. In a way, it is exactly the same as the position of "the South" on slavery, where slavery must triumph over any interest the people of other non-slave states might have.