The ancient Greek word for "bear" was άρκτος.
The Arctic is named after the animal; it's the place where bears are.
Naturally, when you find a place at the opposite side of the globe from the Arctic and where there are no bears, it's the anti-Arctic - in other words, Antarctica.
So the Arctic is Bears Place, and Antarctica is Not Bears Place.
@noelle I was going to say "the arctic bear is the bear-bear" but they named it the polar bear