A glass is full to the brim with water, with an ice cube floating in it

Why

Siya is thinking of the ice as extra water waiting to be added on top of what is already in the glass. But the ice is not sitting outside the water — it is floating IN it, and a floating object pushes aside (displaces) an amount of water equal to its own weight. So the ice has already 'made room' for exactly the water it is made of. When it melts, it turns into precisely that much water, which slots into the space it was already displacing — the level does not rise. Test it: mark the water line on the glass with a pen, let the ice melt fully, and check — the line does not move. (This is also why melting sea ice, which is already floating, does not by itself raise the sea — though ice sitting on land is a different story.) Her brother is right: the level stays the same, because the floating ice was already displacing its own eventual volume of water.