Membrane separation is playing increasingly important role in providing clean water. Simulations predict that membrane pores with strong hydrophobicity produce ultrahigh water permeability as a result of low friction. However, experiments demonstrate that hydrophilic pores favor higher permeability. Herein we simulate water molecules transporting through interlayers of two-dimensional nanosheets with various hydrophilicities using nonequilibrium molecular dynamics. We reveal that there is a threshold pressure drop (ΔP T), exceeding which stable water permeability appears. Strongly hydrophobic pores exhibit extremely high ΔP T, prohibiting the achievement of ultrahigh water permeability under the experimentally accessible pressures. Under pressures < ΔP T, water flows in hydrophobic pores in a running-stop mode because of alternative wetting and nonwetting, thus leading to significantly reduced permeability. We discover that hydrophilic modification to one surface of the nanosheet can remarkably reduce ΔP T by > 99%, indicating a promising strategy to experimentally realize ultrafast membranes.