This is a particularly easy instance since the main factual claim made in the article is true. (Not always the case in discussions of climate issues that you find in the newspaper!) It just happens not to say much one way or the other about global warming.
East Antarctica is four times the size of west Antarctica and parts of it are cooling. The Scientific Committee on Antarctic Research report prepared for last week's meeting of Antarctic Treaty nations in Washington noted the South Pole had shown "significant cooling in recent decades".
Australian Antarctic Division glaciology program head Ian Allison said sea ice losses in west Antarctica over the past 30 years had been more than offset by increases in the Ross Sea region, just one sector of east Antarctica.
"Sea ice conditions have remained stable in Antarctica generally," Dr Allison said.
This is not a "climate change lie exposed" as Whaleoil claims, scientists have known this for a long time and have said so. Now we just have better data. It is not even clear to me that there is "a widespread public belief" that Antartic sea ice is contracting as the article claims. (The Arctic is of course another matter, and maybe many confuse the two?)
Why does increasing Antarctic sea ice not challenge current scientific thinking about global warming? I'll defer to the US agency the National Snow and Ice Data Center
Another important point is that the increase in Antarctic sea ice extent is not surprising to climate scientists. When scientists refer to global warming, they don’t mean warming will occur everywhere on the planet at the same rate. In some places, temporary cooling may even occur. Antarctica is an example of regional cooling. Even our earliest climate models projected that Antarctica would be much slower in responding to rising greenhouse gas concentrations than the Arctic. In large part, this reflects the nature of the ocean structure in Antarctica, in which water warmed at the surface quickly mixes downward, making it harder to melt ice.
In terms of sea ice, climate model projections of Antarctic sea ice extent are in reasonable agreement with the observations to date. It also appears that atmospheric greenhouse gases, as well as the loss of ozone, have acted to increase the winds around Antarctica. Perhaps counter intuitively, this has further protected the Antarctic from warming and has fostered more ice growth.
The one region of Antarctica that is strongly warming is the Antarctic Peninsula, which juts out into the Atlantic Ocean and is thus less protected by the altered wind pattern. The Antarctic Peninsula is experiencing ice shelf collapse and strongly reduced sea ice.
Why are scientists very concerned by reductions in Arctic sea ice but don't seem to talk much about Antarctic sea ice?
Unlike Arctic sea ice, Antarctic sea ice disappears almost completely during the summer, and has since scientists have studied it. Earth’s climate system over thousands of years has been "in tune" with this annual summertime disappearance of Antarctic sea ice. However, satellite records and pre-satellite records indicate that the Arctic has not been free of summertime sea ice for at least 5,500 years and possibly for 125,000 years. So Earth’s climate system and ecosystems, as they exist today, did not develop in conjunction with an ice-free Arctic. Such an ice-free Arctic summer environment would be a change unprecedented in modern human history and could have ramifications for climate around the world.