The first thing to remember is that these are two entirely different ecosystems. There is no global sea ice budget that needs to be balanced. Secondly, we're talking two different measurements: Winter extent in the Antarctic versus summer extent in the Arctic. Theoretically, a better apples-to-apples comparison might be summer extent in the two, but that won't work, and the reason why it won't work gets to the heart of why scientists are much more interested in and concerned by what's happening to sea ice in the Arctic.
The Antarctic is a continent surrounded by ocean. As a consequence, in the summer, sea ice is free to break up and drift northward unimpeded, where the great majority of it melts every summer, climate change or no climate change.
The Arctic is an ocean surrounded by land: There are very few escape routes for the sea ice that forms each winter, and so although some melts each year, some stays, surviving the summer