The Antarctic Peninsula is a very small area that has very clearly been warming substantially over the last few decades, but it represents only 2% of Antarctica. Its local climate is not indicative of the rest of Antarctica or the rest of the Southern Hemisphere, much less of the globe.
Antarctic sea ice extent is actually at the highest levels observed since we started watching it via satellite around 1979. Ice may be shrinking around the Peninsula, but is net growing over the whole continent.