Why must polar molecules be asymetrical? As I understand, polarity in molecules comes from the difference in electronegativity or the ability of the atoms to attract eletrons so the electrons spend more time or are more probable to gravitate more around the atom with stronger electronegativity right? So I wonder why polar molecules must necessarily have an asymetrical structure? (as I've read on multiple sites). Shouldn't a symetrical atom with strong electronegativity with 2 atoms bonded linearly 180° on both sides which are significantly less electronegative, be polar since the electrons would gravitate more towards the center and the sides would then be more positively charged? What am I missing here?



Why is the first molecule (1) not possible? Is it becuase of the less polar atom on the left side repells electrons just as much as the one on the right? But then the electrons would still orbit the middle atom more because its more elctronegative, right?
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.