We simulate the electron transmission through insulating Mylar (polyethylene terephthalate, or PET) capillaries. We show that the mechanisms underlying the recently discovered electron guiding are fundamentally different from those for ion guiding. Quantum reflection and multiple near-forward scattering rather than the self-organized charge up are key to the transmission along the capillary axis irrespective of the angle of incidence. We find surprisingly good agreement with recent data. Our simulation suggests that electron guiding should also be observable for metallic capillaries.