Why are cell membranes selectively permeable?

The hydrophobic center to a cell membrane (also known as a phospholipid bilayer) gives the membrane selective permeability.

Cell membranes are primarily composed of lipid molecules called phospholipids. (Membranes also have many embedded proteins.) Each phospholipid has a hydrophilic head that is attracted to water; these are the white circles in the image below. Each phospholipid also has two hydrophobic fatty acid tails that are repelled by water; these are yellow in the image below. When many phospholipids are put in a watery solution, they therefore spontaneously form spheres called liposomes that point all the water-loving heads toward the water and shield all of the water-fearing tails from it.

The result of the hydrophobic center of the membrane is that molecules that dissolve in water are not capable of passing through the membrane. Charged atoms (ions) and polar molecules such as glucose are repelled by the hydrophobic center of the membrane (these molecules can, however, pass through with the help of membrane protein channels). On the other hand, hydrophobic molecules such as lipids can pass through the membrane, as can small non-polar molecules (such as oxygen gas or carbon dioxide).