why should you never wave people across at pedestrian crossings

You should never wave people across at pedestrian crossings because it can be dangerous. Waving someone across might give them a false sense of safety, as another driver in a different lane or direction may not have seen the pedestrian or your signal and may not be able to stop in time. It’s safer to let pedestrians decide when it is safe for themselves to cross by checking for all oncoming traffic. This avoids confusion and reduces the risk of accidents at the crossing.