There's two main reasons. One is more pragmatic and the other is about long term political interests. The first one is that at the time, cotton exhausted the soil. Plantation crops, especially cotton couldn't keep being planted on the same soil economically. In this period there wasn't as much understanding of soil maintenance and health, and while there was some chemical fertilizer (Daniel Immerwahr's book, How To Hide An Empire gets into the importance to the development of American empire bird guano was b/c of its use as fertilizer) it wasn't as economical to transport into the south and use. So the Southern states constantly wanted new territory to expand to.

The political reason was that free states were expanding. B/c of the Constitutional preferences for slave owners in the Constitution, the South was able to impose their interests on the Northern states. But if the North population kept expanding faster than the south, and if the US added more free states, the South's advantage thanks to the 3/5ths clause would totally disappear and it's stranglehold on the Senate would be gone. At the time of the Civil War, the south had only about 1/3 of the population of the North. On top of that, 1/3 of the South's population was enslaved, so their interests were represented and they gave a representational boost to their enslavers against Northerners. So, if the balance of population kept shifting, the South, already weak in the House, would be totally ignored, and their abuse of minority power in the Senate would be totally sidelined. They had to keep expanding and adding more slave states or become a political non-entity.