Perhaps when he goes to a store to buy ice they price it by the square foot, but everywhere I've been they price it by the pound.
First of all, the evidence for AGW is so overwhelming that the growth of sea in the Antarctic is something to be explained in the context of AGW, not proof against it.
It's a complicated continent, very different from the Arctic -- one a continent surrounded by water, the other water surrounded by continents. The NSIDC has a good page on the differences:
The Antarctic is almost a geographic opposite of the Arctic, because Antarctica is a land mass surrounded by an ocean. The open ocean allows the forming sea ice to move more freely, resulting in higher drift speeds. However, Antarctic sea ice forms ridges much less often than sea ice in the Arctic. Also, because there is no land boundary to the north, the sea ice is free to float northward into warmer waters where it eventually melts. As a result, almost all of the sea ice that forms during the Antarctic winter melts during the summer.(plus more -- read the entire page).
Some think the growth is due to shifts of winds in the southern hemisphere, or increased snowfall on the Southern Ocean, or (Manabe et al's 1992 prediction) an increased supply of water at the near-Antarctic ocean surface that could slightly lower sea surface temperatures. Or there might be a problem with the data model. There doesn't seem to yet be a consensus.
Secondly, ice is measured by volume, not area, because for a given amount of heat, the melting rate varies as the mass changes, which is proportional to the volume change, not the area change. At the risk of being pedantic, recall from high school physics
ΔQ = Hf Δm
where ΔQ is the heat added to the system, m is mass, and Hf is the heat of fusion (334 kJ/kg for ice).
m = density*volume, so
ΔQ ∝ ΔV
(∝ means ("proportional to"). But (being even more pedantic), ΔV is not proportional to the change in area, but (for, say, a block of area A and height h, so V=Ah)
ΔV = hΔA + AΔh
so the change in volume is not proportional to the change in area, but a linear combination of the change in area and the change in height.
This is why, in a warming context, it's accurate to talk about sea ice volume, not sea ice area or extent. The downside, of course, is that we have daily measurements of sea ice area and extent, but only modeled results for sea ice volume. People follow extent because it's the only metric we have, except when papers come out with volume numbers.
Although global sea ice extent is, at the moment, back around 1985 to 1990 levels (though the trend is definitely down), global sea ice volume is much lower than then: PIOMAS calculates Arctic sea ice volume to be decreasing by 260 gigatonnes per year, while Antarctic sea ice is increasing by only 26 Gt/yr.
Arctic sea ice is melting 10 times faster than the Antarctic is gaining sea ice. The Earth is now losing over a trillion tonnes of ice a year.
When talking about warming, viz. the energy imbalance of the Earth, the volume of ice is the appropriate metric, not its area.