States’ rights yes but specifically the right of new states entering the union to permit slavery. The North sought to limit or even prevent the expansion of slavery into the territories, which would lead to congress being dominated by the South. The South hoped to gain leverage and forge policies that favored their largely agrarian economy. The issue of slavery was not an add-on. It was key, although not so much as a moral issue as an economic one. The abolitionist movement of course fueled the sentiments for emancipation on moral grounds, but they didn’t cause the war.
And this is the grand prize winning point. Slavery could not actually expand into any territory because plantation farming was simply impossible in the territories. The feared "expansion" was all theoretical, but in real terms, was actually impossible to any significant degree.
The real situation in 1860 was that the Northern dominated congress had rigged the laws so that the Southern states were producing 73% of all the federal revenue and the bulk of that money was being spent in the Northern states, especially for railroads. Also the laws forced the Southern states to transport their export goods through well connected Northeastern shipping companies, banks, insurance, warehousing, ect at far greater costs than they would incur if they were able to use foreign shipping.
Basically the Northern states were taxing the sh*t out of them and gouging them for other services which the Northern dominated congress had written into law. (Such as the "Navigation act of 1817")
From sources I have read, about 60% of all the production of the Southern states ended up in the hands of the North Eastern power barons and their Washington DC corruptocrats.
And therefore they wanted to keep control of Congress away from the hands of the Southern states.
Northerners first learned that slavery was morally wrong in their churches, in what's been called the Second and Third Great Awakenings.
It's why they first abolished slavery in their own states.
But having abolished slavery in their own states, most Northerners were still content to let it continue in the South, regardless of moral concerns because of obvious economic benefits to the nation as a whole.
Still, Northern workers did not wish to compete with slaves in the western territories, for both economic and moral reasons, and that was the rock on which the Union broke.
But the key element which flipped the majority of Northerners from Democrats tolerant of Southern slavery into anti-slavery Republicans came from the threat represented by the US Supreme Court's Dred Scott decision -- fully understood, it meant slavery could not be constitutionally abolished anywhere.
As Abraham Lincoln said at the time:
Expanding slavery into the Territories was the Right they were talikng about.