Recent experiments have revealed that random zwitterionic amphiphilic copolymer (r-ZAC) membranes exhibit excellent Cl-/F- permselectivity circumventing the solubility-diffusivity trade-off. We conducted molecular dynamics simulations to investigate the origin of the experimental results on the transport of sodium halides in r-ZAC membranes. Our results indicate that the enhancement of Cl-/F- diffusivity selectivity in r-ZAC membranes (relative to that in bulk water) stems from the increase in dielectric drag dominating over the increase in Stokes drag, zwitterionic group-induced steric hindrance, and ion-polymer interactions. The importance of dielectric drag is further demonstrated by showing that reduction in ionic charges leads to a complete reversal of the diffusivity selectivity trends. We conclude that leveraging the impact of hydrophilic nanoconfinement on the dynamics of water can be utilized as a strategy to simultaneously augment solubility selectivity and diffusivity selectivity for separations, wherein the flux of the larger ionic species is desired over that of the smaller.