I understand that Eli Whitney was marginal, but he invented the cotton gin. At the time of it's invention, the industry of slavery was failing. Demand for the goods produced in the south was falling, and slavery was simply becoming too expensive to make sense. Then, here comes the cotton gin. It made cotton make sense, in large quantities. Slavery was virtually reborn by the cotton gin. Though no one can say what would have happened without it, the boom in slavery was caused directly by the newfound ease of de-seeding cotton with the cotton gin. So whether it was Whitney or someone else, the cotton gin was really responsible for slavery's comeback, and that's when the south began to be extremely dependent on it. And you won't disagree that the Civil War was fought over slavery, will you, even if there were other marginal issues?
Now I'm not saying Eli Whitney is solely responsible for the Civil War, he was definitely a contributor, and without his invention of the cotton gin, the war may have been put off for a bit longer, or avoided entirely.