Arctic and Antarctic don't mean anything about actual bears. They are named after the Ursa Major constellation. The absence of bears in Antarctica is a coincidence.
Ursa Major means "the great bear“, though. Being named after something that's named bear counts in my book as well as those of all but the worst pedants.
The absence of bears in Antarctica is a coincidence.
That's what the secretly hyper-intelligent penguins who scared away the polar bears WANT you to think!