We report molecular dynamics simulations of the electrowetting behavior of liquids in confinement between two oppositely charged graphene sheets. We observe that changes in the static contact angles of water, salty (4 M NaCl) water, and 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) (a room temperature ionic liquid) exhibit an asymmetric dependence on electric field polarity. The solid-liquid interfacial tension, which is expected to drive these changes, has been calculated independently by integrating the reversible work performed upon introducing positive and negative surface charges. This quantity shows either no dependence on the polarity of the electric field (water) or a dependence exactly opposite to the one obtained by applying the Young-Lippmann equation to the observed contact angles ([bmim][BF4]). Our analysis indicates that the observed contact angle asymmetry finds its origin in the liquid structure in the vicinity of the three-phase contact line. In particular, it is suggested that the molecular orientation properties are crucial to determine the asymmetric wetting behavior of pure water; in addition, the contrast in the strength of the ion hydration shells has a decisive influence on the NaCl solution behavior.