Pressure signals measured at the throttled flow of oscillating valves show a double peak when the closing and reopening of the clearance occur in short times. This phenomenon has been evidenced in spring-loaded valves or in valves of biological flows such as vocal-fold collision upon glottal flow. A comprehensive study of the fluid dynamical causes of this flow behavior is still pending. This work considers a valve with a simple geometry and a prescribed evolution of gap height with time. High performance numerical simulations in two dimensions and simplified models are used to explain experimental results and undertake a parametric study. A reversal of the longitudinal volumetric flow direction near the entrance and exit of the channel at closing and reopening, named suction-cup effect, is shown to be associated to the double peak presence in pressure signals.