Because the South believed that more Free States were going to be admitted to the Union and that would result in there being enough States so that an abolition amendment could be adopted without any Slave State ratifying.
As for the economic argument, slavery was key to the antebellum South's economy. To abolish slavery was to collapse the Southern economy. So when it came to the antebellum South, the economy and slavery were fundamentally linked. Also, remember the Southern States cited slavery as their principal reason for seceding.
They could not have passed the original 13th amendment if the Southern states weren't forced to vote for it. If you add the 11 Confederate states to the 5 Union slave states, you have 16 slave states that would not have voted for such an amendment absent the war. That meant there would have to be 64 states in the Union to achieve a 3/4ths majority against the 16 slave states. For just the 11 states to remain in opposition, there would have had to be 44 states in the Union before they could have passed such an amendment. That was many years in the future.
That wasn't a realistic possibility at the time.
As for the economic argument, slavery was key to the antebellum South's economy.
It also provided 3/4ths of the revenue to fund the Federal Government. Also 40% of it's slave earned income was siphoned off by New York.
To abolish slavery was to collapse the Southern economy. So when it came to the antebellum South, the economy and slavery were fundamentally linked.
Yes, but Washington D.C. and New York were okay with this so long as the money kept flowing into their control. What drew the ire of Washington was not only the cessation of this slave earned money, but the possibility the South would capture the European trade instead of New York dominating it. 3/4ths of all European money was earned by Southern exports, but the way the laws were jiggered, almost all the returning imports came back through New York. (Tariffs were just as high in Charleston, and it was 800 miles further South. No reason to go there without some economic incentive such as higher profits.)
Also, remember the Southern States cited slavery as their principal reason for seceding.
Some of them did. Most of them did not. Some of them cited economic arguments and the unfair manner they felt they were being treated by the North East and Washington.