[al-king]

While it's certainly named for bears, that appears to be be a folk etymology: as the Wikipedia article you link suggests, the Arctic is named for the northern bear constellations Ursa Major and Ursa Minor, so called since the time of Homer. The word Antarctic has been in English since the C14th ( http://www.etymonline.com/index.php?term=Antarctic ); a continent opposite to the Arctic was hypothesised long before Antarctica was discovered in the 17th century. Antarctic, then, means "opposite of north" rather than "no bears" - though I suppose the Ursa constellations were also not in the north :) and it's a nice mnemonic.