The nature of neutrinos, whether Dirac or Majorana, is hitherto not known. Assuming that the neutrinos are Dirac, which needs B − L to be an exact symmetry, we make an attempt to explain the observed proportionality between the relic densities of dark matter (DM) and baryonic matter in the present Universe i.e., ΩDM ≈ 5 ΩB. Assuming the existence of heavy SU (2)L scalar doublet (X = (X 0 , X − ) T ) in the early Universe, an equal and opposite B − L asymmetry can be generated in left and right-handed sectors by the CP-violating out-of-equilibrium decay X 0 → νLνR since B − L is an exact symmetry. We ensure that νL − νR equilibration does not occur until below the electroweak (EW) phase transition during which a part of the lepton asymmetry gets converted to dark matter asymmetry through a dimension eight operator, which conserves B −L symmetry and is in thermal equilibrium. The remaining B − L asymmetry then gets converted to a net B-asymmetry through EW-sphalerons which are active at a temperature above 100 GeV. To alleviate the small-scale anomalies of ΛCDM, we assume the DM to be self-interacting via a light mediator, which not only depletes the symmetric component of the DM, but also paves a way to detect the DM at terrestrial laboratories through scalar portal mixing.