Comparing apples to apples, it isn’t.
The yearly average, east-west average temperature at sea level near Antarctica is almost the same as at the equivalent latitude in the Arctic. See Figure 5.7 [here](http://weatherclimatelab.mit.edu/wp-content/uploads/2017/07/chap5.pdf): the temperature at say 65 degrees south (near the coast of Antarctica) averages -5 C, identical to 65 north (northern Alaska).
But the South Pole is much much colder than that, and the figure I linked shows why: it’s at 10,000 feet (3 km) altitude. **South Pole station sits on top of a giant continent-sized mountain of ice, and it’s cold on top of a mountain.** You can see in the linked figure that the temperature at 90 south at 680 mbar (the pressure-height of South Pole Station) averages -30 C, almost identical to the North Pole at the same altitude.
It’s nothing to do with ocean currents or whatever: it’s just a matter of altitude.
The Arctic is all ocean (edit: the north pole… obviously there is land north of the arctic circle, but I’m talking about the extreme high arctic, which I think is what is referenced in the question). There’s a large ice cap, but it’s frozen sea water. And, while the ocean up there is quite cold, it’s not THAT cold, because the ocean retains a tremendous amount of energy, and it’s always circulating. This moderates the temperature of the Arctic to an extent. Antarctica, by contrast, is a huge continental landmass. Just like in more familiar areas, when you get away from the coast, you lose the moderating effects of the ocean. So, once inland, there is nothing to moderate the intense polar cold, so it gets cold and stays cold. In addition, the thickness of the sea ice in the arctic is some 10-20 feet thick. So, even when standing at the north pole, you’re basically at sea level. Antarctic is covered by an immense continental scale ice sheet that tops out at 15 THOUSAND feet thick. This ice sheet is so thick that Antarctica is actually the highest continent on Earth. So… in addition to not having the moderating effects of ocean water in Antarctica, you are also at high elevation. Either of these alone makes for quite a lot of cold – add them together and you have the kind of cold that makes the Antarctic like another planet.
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