HfO_{2}-based ferroelectric thin films are promising for their application in ferroelectric devices. Predicting the ultimate magnitude of polarization and understanding its switching mechanism are critical to realize the optimal performance of these devices. Here, a generalized solid-state variable cell nudged elastic band method is employed to predict the switching pathway associated with domain-wall motion in (Hf,Zr)O_{2} ferroelectrics. It is found that the polarization reversal pathway, where threefold coordinated O atoms pass across the nominal unit-cell boundaries defined by the Hf/Zr atomic planes, is energetically more favorable than the conventional pathway where the O atoms do not pass through these planes. This finding implies that the polarization orientation in the orthorhombic Pca2_{1} phase of HfO_{2} and its derivatives is opposite to that normally assumed, predicts the spontaneous polarization magnitude of about 70 μC/cm^{2} that is nearly 50% larger than the commonly accepted value, signifies a positive intrinsic longitudinal piezoelectric coefficient, and suggests growth of ferroelectric domains, in response to an applied electric field, structurally reversed to those usually anticipated. These results provide important insights into the understanding of ferroelectricity in HfO_{2}-based ferroelectrics.