Most protein molecules do not adsorb onto ice, one of the exceptions being so-called antifreeze proteins. In this paper, we describe that there is a force pushing an antifreeze protein molecule away from the ice surface when it is not oriented with its ice-binding plane toward the ice and that this pushing force may be also present even when the protein is oriented with its ice-binding plane toward the ice. This force is absent only when certain specific distance criteria are met, regarding the surface of ice and the protein. It acts at early stages of adsorption, prior to the solidification of water between the ice and the protein molecule nearby. We propose the water-originating mechanism of the generation of this force and also the mechanism of remote attachment of an antifreeze molecule to the ice surface. In liquid water, there exist locally favored structures, ordered and of high specific volume. The presence of a protein molecule usually shifts the equilibrium that exists in liquid water toward increasing the number of high-density, disordered structures and diminishing the number of low-density structures. Creation of the locally favored structures may be hampered not only near the non-ice-binding surfaces but also between the ice surface and the protein surface, if the distance between these surfaces does not allow these structures to develop because the available space is not sufficient for their proper formation. This conclusion is supported by the analysis of the mean geometry of a single hydrogen bond, as well as of the hydrogen bond network in the solvation layer and a structural order parameter that characterizes the separation between the first and second solvation shells of a water molecule.