The electrowetting behavior of 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) confined between two oppositely charged graphene layers is investigated using molecular dynamics simulations. By introducing charges on the surface, counterions are attracted to the surface and co-ions ate repelled from it, leading to the reduction of the solid-liquid interfacial free energy and consequently the contact angle. Recently, we have shown that changes in the contact angle upon charging the surface are asymmetric with respect to surface polarity and opposite to the changes in the solid liquid interfacial free energy. In this work, the asymmetry of the solid-liquid interfacial free energy is shown to originate from differences in structural organization of the ions at the interface, with positively polarized surfaces inducing a more favorable electrostatic arrangement of the ions. Analysis of the liquid structure in the vicinity of the three phase contact line, however, shows that the ion size asymmetry, together with differences in orientational ordering of the cations on oppositely polarized surfaces, instead leads to enhanced spreading on the negatively polarized surfaces, resulting in a corresponding contact angle asymmetry.