Everybody at the time believed this, on both sides of the issue.
I'm not so sure. There was no particular reason slavery couldn't have gone on being economically profitable in the South, at least if they changed some of their farming practices that essentially mined the soil.
Plantation agriculture wasn't going to expand much into the territories anyway. Tough to grow cotton in Nebraska.
That's why for the real pro-slavery guys secession was only the first step. After breaking away from the Union, they intended to conquer Latin America and impose slavery on nations most of which had already outlawed it.
They also planned to start the African slave trade up again. Of course, the Royal and US Navies might have had some input on the practicality of that idea.
That was not the issue as much as demographics were. The slave population grew far faster than the white population. By 1860, several of the deep South states had larger slave than free populations. That was fine -- to a point, as long as the demand for slaves in newly settled areas continued. The delemia of the slave economy was two fold. First, minus expansion, with a rapidly increasing supply of slaves and a deminishing demand as the plantation system reached its geographical limits, the value of slaves would plumet destroying the largest single source of wealth in the deep south especially.
Secondly, slavery contained within its current limits would have over another generation or so placed the ever smaller white population in very great risk from a hostile black population. Expansion was also a safety valve that kept the slave populations within controllable limits.
Lincoln and the Republican party's opposition to the further expansion of slavery is what drove the south into secession. They saw their lives and fortunes at risk if slavery were to be contained.
Tough to grow cotton in Nebraska.
True, but the gold, silver and copper mines of the west would have been worked by slaves instead of free men if the Slaveocracy had their way with expansion.