The economic argument for slavery was that it was necessary and profitable. It was seen as necessary because it would have been very hard (if not impossible) to get free people to do the work needed for things like raising cotton, particularly early on when there was a lot of free or cheap land where people could have their own farms. In addition, it was economical because, after all, you didn't have to pay the workers.
The argument against slavery is that it was less efficient than a system of free laborers would have been. Slaves had no incentive to work hard. In fact, they would try to work as slowly as possible. They would also do things like breaking tools as a way to resist their owners. Free laborers would have worked harder and therefore they would have produced more and plantation owners would have gotten higher profits.