"While the North Pole has been losing sea ice over the years, the water nearest the South Pole has been gaining it."

Misleading or inaccurate. The AMOUNT of sea ice in the Antarctic has been declining. The AREA of sea ice in winter has been rising. But area is NOT volume or mass or quantity. Area is a two dimensional term.

http://tinyurl.com/9m8wz9j

Basically, change in wind patterns due to a stronger circumpolar jet stream and ozone depletion cooling have made it easier to FORM first year ice in the winter (cooler outflowing winds vs warmer inflowing winds). The overall trend is a longer 'sea ice season'(the Antarctic is no real amount of SUMMER sea ice) with thin first year ice of no more than a meter thickness.

"Shifts in wind patterns and the giant ozone hole over the Antarctic this time of year _ both related to human activity _ are probably behind the increase in ice, experts say."

Just so.
http://tinyurl.com/9u9dlgj

The reason that the ice is thinner despite the longer 'growing season' is because the air and water temperatures are higher, making it harder to create thick ice.

"It sounds counterintuitive, but the Antarctic is part of the warming as well."

Mainly because of using an incorrect 'metric' to relate temperature trends to climate. Winter ice area is meaningless as there is no sun to reflect or absorb insolation. Only the summer extent makes much difference and the minimum is pretty consistently near zero.