When two solids start rubbing together, frictional sliding initiates in the wake of slip fronts propagating along their surfaces in contact. This macroscopic rupture dynamics can be successfully mapped on the elastodynamics of a moving shear crack. However, this analogy breaks down during the nucleation process, which develops at the scale of surface asperities where microcontacts form. Recent atomistic simulations revealed how a characteristic junction size selects if the failure of microcontact junctions either arises by brittle fracture or by ductile yielding. This work aims at bridging these two complementary descriptions of the onset of frictional slip existing at different scales. We first present how the microcontact failure observed in atomistic simulations can be conveniently "coarse grained" using an equivalent cohesive law. Taking advantage of a scalable parallel implementation of the cohesive element method, we study how the different failure mechanisms of the microcontact asperities interplay with the nucleation and propagation of macroscopic slip fronts along the interface. Notably, large simulations reveal how the failure mechanism prevailing in the rupture of the microcontacts (brittle versus ductile) significantly impacts the nucleation of frictional sliding and, thereby, the interface frictional strength. This work paves the way for a unified description of frictional interfaces connecting the recent advances independently made at the micro- and macroscopic scales.