why do nonpolar molecules, such as cholesterol, repel water?

The covalent bonds of lipids create a small charge that repels water molecules.

This is because polar compounds bind both positive and negative particles to them, while nonpolar molecules attract only the electrons in their chemical bonds (i.e., negatively charged).

Nonpolar molecules are insoluble in water due to the natural incompatibility of their structures, as well as due to the electrical charges created by these structures. Nonpolar liquids will not mix with non-water solvents because they do not dissolve easily. Non-aqueous solvents typically have hydrophobic (fear/dislike) bonds at the surface; this prevents contact with other substances such as other hydrocarbons, oils and fats