Lithium metal anodes hold great promise for next-generation high-energy-density rechargeable batteries due to their high theoretical capacity and low electrochemical potential. However, practical implementation is severely hindered by uncontrolled lithium dendrite growth during repeated plating and stripping, which leads to capacity fading, low Coulombic efficiency, increased internal resistance, and, in severe cases, internal short circuits caused by dendrites penetrating the separator and contacting the cathode. Although it has long been recognized that the solid electrolyte interphase (SEI) plays a key role in lithium plating instability, it is often oversimplified or neglected in conventional theoretical analyses. As a result, commonly used stability indicators, such as the limiting current density, frequently fail to predict experimental observations, where mossy lithium dendrites are routinely formed well below theoretical thresholds. We develop a phase-field model that incorporates key SEI effects, including transport, evolution, and fracture, to study lithium plating instability. Our simulations, performed under experimentally relevant conditions, show that competition between lithium plating and SEI self-healing leads to incomplete SEI coverage. The coexistence of two distinct ion-transport pathways, the slow transport through intact regions and the fast transport through fractured areas, impacts the local plating behavior. The findings identify the SEI rupture and incomplete recovery as key mechanisms promoting mossy dendrite formation, thereby resolving discrepancies between experimental observations and prior theoretical predictions.