I'll try to add to what
@jgoodguy has said. Most southern ports weren't very deep, couldn't accommodate many ocean-going vessels, and definitely didn't have the facilities to deal with international shipping so the bulk had to go to places like New York and Boston, be warehoused, and parceled out by factors to the ships that carried it to Europe. Southern ports mostly dealt with smaller vessels that ran up and down the coastline carrying "stuff" to and from the large northern ports. Also, large banking houses and insurance companies didn't exist in the south and those were necessary for international trade. Dealing directly with foreign buyers was just not practical.
It's the subject of a different thread but in reality the profit from plantation agriculture and it's slave labor was close to equally shared by northerners and southerners before the war. If you've not read it I recommend: Farrow, Anne, Joel Lang, and Jefifer Frank (2005).
Complicity: How the North Promoted, Prolonged, and Profited from Slavery. It discusses some of these things. Port depths and facilities are also discussed in: Wise, Stephen R. (1988).
Lifeline of the Confederacy: Blockade Running During the Civil War.