In organic chemistry we recently learned something about chemical reactions: A reaction between two symmetrical (achiral) molecules will always yield either a symmetrical product or equal mixtures of two mirror images (racemic mixtures). A reaction involving asymmetrical (aka chiral) molecules may yield any possible product. Thus symmetry is always preserved, but asymmetry may yield symmetry.
Given billions of years of chemical reactions, regardless of what molecules we started with it would seem that we are proceding toward symmetry. Does this mean that the universe must be composed entirely, or virtually entirely, of some combination of achiral molecules and racemic mixtures?