I am pretty sure all Antarctica cruises leave from Ushuia, Chile (sorry if I mucked up the spelling).
They then spend two days creossing through the Starits of Magellan known for high seas.
Those who can afford it fly to Elephant Island and pick up the ship after the potentially rough spot, but they don't have an international airport and I have not heard of any ship basing out of there.
Some go to Antarctica from the east coast. I guess, such as from Buenos Aires and maybe hit the Falklands first.