If you think slavery was the main, or even a large driver of industrial growth, you need to explain the extreme lack of industry in places where slavery was common versus places where there was no slavery. E.g., New England versus the Carolinas, etc.
Northern manufacturing bought cotton from slave plantations, yes. As did British mills.
However, you'll note that in the absence of southern cotton during the Civil War, these textile mills did not shut down or become unprofitable, they switched to alternate sources of cotton.
