Ah! I think I know the source of confusion here :)
Did you know there are 3 types of ice in Antarctica? Ice shelves attach to land, but jut out over the sea. Then you have land-ice (glaciers and the like, which are constantly moving, but very slowly), and of course sea ice, which is free floating in the ocean.
The ice we are concerned with are *ice shelves*. When ice shelves break apart and fall into the sea, sea level rises, because this is now *new ice* (and eventually new water) that the ocean is supporting. Melting sea and land ice (while problematic indicators for other reasons) aren't as bad because they don't change sea levels. Gigantic ice shelves, breaking into the ocean are VERY VERY BAD.
What can happen? Not just changing sea levels, but changing sea temperatures and therefore changing sea circulation. If the ocean doesn't circulate, we won't have currents, and you can imagine what a disaster that would be (ecologically, for trade routes, etc).
If ice interests you, (or if you just want information on how Antarctica is linked to climate change), I point you to ANDRILL's (ANtarctic geological DRILLing) website:
They've got great educational resources there, including short video clips in addition to text and pictures.
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