Why is the hydrogen bond different from other bonds that allows ice to float in water rather tan sink. I don't want the math. I want the reason that bond is different than the rest. Why, not how.
The reason is that when in crystalline form, water molecules are arranged in a tetrahedral structure kept together by hydrogen bonds (see figure below).
This structure results in an increased average distance between water molecules, as shown in this schematic representation:
Quoting from J. Kotz, Chemistry and Chemical reactivity:
One reason for ice’s unusual structure, and water’s unusual properties, is that each hydrogen atom of a water molecule can form a hydrogen bond to a lone pair of electrons on the oxygen atom of an adjacent water molecule. In addition, because the oxygen atom in water has two lone pairs of electrons, it can form two more hydrogen bonds with hydrogen atoms from adjacent molecules. The result is a tetrahedral arrangement for the hydrogen atoms around each oxygen, involving two covalently bonded hydrogen atoms and two hydrogen-bonded hydrogen atoms. To achieve the regular arrangement of hydrogen-bonded water molecules linked by hydrogen bonding, ice has an open-cage structure with lots of empty space. The result is that ice has a density about 10% less than that of liquid water, which explains why ice floats.
This peculiar property is shared by other substances with a tetrahedral solid structure, like silica (SiO$_2$), and also by some elements like Si, Ga and Ge. Notice that the crystal structure of Si and Ge is the fcc diamond cubic, which also has a tetrahedral coordination (figure below):
It seems therefore that a crystal structure with a lower density than the corresponding liquid is favored by those elements/compounds with a tetrahedral coordination (Ga being an exception, with its orthorhombic structure).
Note that however that hydrogen bonds or tetrahedral coordination are not sufficient to have this property, as you can see for example from the fact that there are some high-pressure ice polymorphs, such as ice II, ice III, high-density amorphous ice (HDA), and very-high-density amorphous ice (VHDA), with higher density than liquid water. Many factors contribute to this effect, and there is no general easy rule.