Why must polar molecules be asymetrical?
If you start with the wikipedia definition of chemical polarity, which is standard (if not IUPAC) usage:


  In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end. 


then it's not hard to understand why a molecule such as $\ce{CO2}$ containing a center of inversion lacks a dipole moment and is therefore "nonpolar", as are, by this definition, other molecules with high symmetry properties and lacking a net dipole moment:


  The only groups compatible with a dipole moment are Cn, Cnv and Cs. In molecules belonging to Cn or Cnv the dipole must lie along the axis of rotation.