I would highly recommend Roger L. Ransom's short but masterful essay "The Economics of the Civil War" for some perspective.

Slavery for the United States in 1860 was far from a tangental undertaking. Some 4 million people were owned as slaves in the United States, making up almost 13% of the total population, and 40% of the population of the eleven states that would go on to secede and form the Confederacy in 1861. More than half the agricultural labor in these Southern states were slaves, and their combined value is estimated at $3 billion dollars, worth more than all the agricultural farmland and farm buildings in those states (historian David Blight says the combined value of US slaves was more than all US manufacturing and railroads).

Slavery directly benefited the white population of the Southern states, but also indirectly benefited other regions of the US as well. Something like half of US exports in 1860 were slave-produced cotton, and this benefited Northern merchants (especially in New York City) who arranged the sale, and textile manufacturers in New England and Britain who purchased the ever-lower cost and ever more abundant cotton for their mills. Cotton exports helped to finance imports of manufactured goods from places like Britain, and imported tariffs provided the majority of revenue for the US federal government at the time.

Not only was the product of American slavery processed through increasing technological advancements in the textile industrial revolution, but technological advance had made greater slavery in the South possible in the first place: Eli Whitney's "cotton gin" of 1793 allowed for the faster processing of "short staple" cotton in the American South, which led to a vast expansion of cotton production and a consequent expansion of slavery.

With the conquest of northern parts of Mexico in 1848 and the annexation of Oregon Country, there was an increased focus in national politics on how these Western lands would be settled: would they be open to slavery, or settled by free laborers? This was the period when "Free Soilers" began to fear the negative impact fo expanding "slave power" - if slavery were allowed into Western territories, that it would have negative impacts for white settlers looking for paid labor. In turn, Southern slaveholders had increasing speculation in their human property - slave prices rose at a constant rate from the 1840s onwards, and was followed by a growth of the slave population. Slaveowners ultimately felt that slavery had to expand if the Southern states weren't to be left with a "surplus" slave population. This led Southerners to push for allowing slavery into new Western territories and for the expansion of US control into the Caribbean (the 1854 Ostend Manifesto proposed that the US offer to either buy or conquer Cuba from Spain and make it a slave state). There are a lot of other twists and turns but this is the ultimate conflict that brought about the 1860 crisis and subsequent Civil War.

I would dispute the idea that slavery in 1860 was an "antiquated and morally bankrupt practice." True, Britain had granted full emancipation in the West Indies in 1838 and France in 1848 (although it would continue in other colonies of theirs for longer, for example through the "blackbirding" of Polynesians into the late 19th century). And most Spanish-speaking republics had abolished slavery by 1860. But in that year slavery was still very much legal in the Spanish American colonies of Cuba and Puerto Rico, as well as in the Empire of Brazil. Cuba would not see slavery abolished until 1886, Brazil until 1888.

Nor did all Americans see slavery as a "morally bankrupt and antiquated practice". Certainly, abolitionists would have felt that way, but the majority of whites in free states were not abolitionists at the time. If anything, as can be seen in the Free Soil movement, the fear was that slavery would expand and overwhelm free labor - quite the opposite from seeing it as an ancient vestige.

Southern slaveholders were even more explicit. George Fitzhugh in his 1857 book Cannibals All went so far as to argue that Southern slavery was such a beneficial institution that it should be applied to poor white Northerners instead of "wage slavery" (his was an extreme position, but not a disreputable one among Southerners). Numerous Southern states in their declarations of secession, such as South Carolina's, were explicit in their belief that secession was to defend the institution of slavery, and that slavery was an unambiguous good.

Most famous, perhaps, is the so-called "Cornerstone Speech" by Confederate Vice President Alexander Stephens:

Our new government ... its foundations are laid, its corner- stone rests, upon the great truth that the negro is not equal to the white man; that slavery subordination to the superior race is his natural and normal condition. This, our new government, is the first, in the history of the world, based upon this great physical, philosophical, and moral truth.

So, in summary: slavery integral not just to the regional economy of the Southern Slave states, but to the national economy of the United States as well (and arguably to industrializing parts of Europe like Britain). Slavery made technological and economic advances possible, and in turn benefited from technological advances. Although abolition of slavery was gaining some favor in parts of Europe and the Americas, it was very far from a dying institution, nor did Americans in 1860 see it as such.

Sources (in addition to the linked ones):

Daniel Walker Howe What Hath God Wrought: The Transformation of America, 1815–1848

James McPherson Battle Cry of Freedom: The Civil War Era