There is some truth to that.
The south wanted to secede NOT JUST to keep slavery, but to protect states rights.
They did not think The Federal Government should be telling states they had to stop owning slaves. (Remember - it was a world-wide accepted practice before those times. Some people actuall SOLD THEMSELVES into slavery because it was a guaranteed job and food and shelter.)
Imagine if instead of slavery they fought over the government forcing them to, oh.. I dunno.. buy health insurance?
But neither slavery nor states rights were in any way threatened in November 1860 when Deep South Fire Eaters began organizing to declare secession.
In fact, they still ran the show in Washington DC, through their Doughfaced puppet, President Buchanan.
So they declared their secessions "at pleasure" in anticipation of what the Federal Government might do at some future time, now that "Ape" Lincoln and his "Black Republicans" were coming to office, in March 1861.
We know that even into the late 1850’s the abolitionists were a minority voice, so there was no one of import or office that was “telling states they had to stop owning slaves”. Certainly not the Lincoln administration. There were voices who continued to object to the expansion of slavery into the western territories - as there had been since the nations founding.
The only “states rights” that the southern states ever demanded was the right to keep slavery, expand slavery, and compel northern states to be an unwilling partner in the Peculiar Institution.
As to the status-quo of slavery internationally, the United States was one of the very last civilized countries to prohibit the practice.