Recent experimental work has suggested that electroosmotic flows (EOFs) through conical nanopores exhibit rectification in the opposite sense to the well-studied effect of ionic current rectification. A positive bias voltage generates large EOF and small current, while negative voltages generate small EOF and large current. Here we systematically investigate this effect using finite-element simulations. We find that inside the pore, the electric field and salt concentration are inversely correlated, which leads to the inverse relationship between the magnitudes of EOF and current. Rectification occurs when the pore is driven into states characterized by different salt concentrations depending on the sign of the voltage. The mechanism responsible for this behaviour is concentration polarization, which requires the pore to exhibit the properties of permselectivity and asymmetry.