I'm not the brightest bulb in the box so maybe my reasoning is faulty. If you fill a glass with ice and water to the very rim and set it out so the ice melts, as the ice melts the water level does not rise to overflow the glass.
What am I missing?
FWIW, you are correct. The level of the liquid in a container full of ice and water will not rise as the ice melts. Due to the expansion water experiences when freezing, ice displaces roughly 7% less volume than the water that makes up the ice.
So roughly 7% of a piece of ice sticks up above the level of the surrounding water. As the ice melts there is less of it floating above the level of the surrounding liquid water, and when the ice is completely melted the level of the water will remain the same. This is a basic physics principle of buoyancy.
The ASSUMPTION behind your post is that the ice in question is floating in the water. However, the theory of the climatologists is that the polar ice caps that are melting are NOT floating in the water - they are sitting on solid land. So as that ice melts the water from the ice caps will run off into the surrounding oceans and thereby RAISE the level of the water.
Unfortunately for these climatologists, this has NOT proven to be the case. The ocean levels have not raised appreciably in the short period of time that humans have been recording such measurements. What's more, a fair number of the same people who are most loudly and vehemently proclaiming the impending doom of rising ocean levels brought on by climate change, are at the same time also buying ocean-front property in locations like Martha's Vineyard.
That begs the question: if they REALLY believe the oceans are rising due to climate change, and that the coastal areas of the exiting continents will soon be flooded as a result, then why the HELL are so many of them buying multi-million dollar coastal estates that, according to their claims about climate change, will soon end up UNDERWATER? It just doesn't make sense.
Something about this picture just doesn't pass the "sniff-test".
Either they don't believe the theories they are pushing about climate change raising the levels of the oceans, which means they are LYING to us, or they are idiots to be investing in ocean-front properties which will soon be underwater. Either way this brings up the question of whether or not we should rely on their judgement about such matters.
THEY can't have it BOTH ways...