Rare earth elements (REEs) are widely used in several electrical and electronic devices and emerging technologies. With increase in demand of REEs, their recovery from electronic wastes, through hydrometallurgical routes, is a promising alternate source of these elements over conventional mining processes. In a number of experiments, organophosphoric acid ligands such as bis-2-ethylhexyl phosphoric acid (D2EHPA) and 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (EHEHPA) have shown high selectivity toward heavier REEs. While the general extraction equilibrium is well established, an atomistically detailed understanding of the origin of this selectivity is still lacking. We use molecular dynamics simulations to elucidate the structure of the Nd- and Dy-D2EPHA complexes in vacuum, aqueous, and organic phases and show that the selectivity of D2EHPA for Dy arises from the favorable differential stabilization of the complex in the solvent phases, caused by the structural features of the Dy-D2EHPA complex. To complement our simulations, solvent extraction experiments were carried out on a 4:1 mixture of Nd- and Dy ions in chloride media, representative of their ratios found in NdFeB magnets, with n-heptane as the diluent. Though the concentration of Dy is four times smaller, we show that the selectivity of D2EHPA toward Dy can be exploited to obtain enhanced separation in a two step process by first extracting Dy at low pH and starving doses of D2EHPA, followed by the extraction of Nd at higher pH. Our work gives important insights into the atomistic origins of the selectivity of phosphoric acid ligands, which is essential in the design of newer ligands or ligand combinations to obtain enhanced separation of REEs from e-wastes and eventual commercialization of the process.