Electrical breakdown simulations are carried out for liquids in response to a sub-microsecond (∼100-200 ns) voltage pulse. This model builds on our previous analysis and focuses particularly on the polarity effect seen experimentally in point-plane geometries. The flux-corrected transport approach is used for the numerical implementation. Our model adequately explains experimental observations of pre-breakdown current fluctuations, streamer propagation and branching as well as disparities in hold-off voltage and breakdown initiation times between the anode and cathode polarities. It is demonstrated that polarity effects basically arise from the large mobility difference between electrons and ions. The higher electron mobility leads to greater charge smearing and diffusion that impacts the local electric field distributions. Non-linear couplings between the number density, electric field and charge generation rates then collectively affect the formation of ionized channels and their temporal dynamics.