Aqueous binary mixtures have received immense attention in recent years because of their extensive application in several biological and industrial processes. The water-ethanol binary mixture serves as a unique system because it exhibits composition-dependent alteration of dynamic and thermodynamic properties. Our present work demonstrates how different compositions of water-ethanol binary mixtures affect the pair hydrophobicity of different hydrophobes. Pair hydrophobicity is measured by the depth of the first minimum (contact minima) of potential of mean force (PMF) profile between two hydrophobes. The pair hydrophobicity is found to be increased with addition of ethanol to water up to a mole fraction of xEtOH = 0.10 and decreased with further addition of ethanol. This observation is shown to be true for three (methane-methane, isobutane-isobutane, and toluene-toluene) different pairs of hydrophobes. Decomposition of PMF into enthalpic and entropic contribution indicates a switch from entropic to enthalpic stabilization of the contact minimum upon addition of ethanol to water. The gain in mixing enthalpy of the binary solvent system upon association of two hydrophobes is found to be the determining factor for the stabilization of contact minimum. Several static/dynamics quantities (average composition fluctuations, diffusion coefficients, fluctuations in total dipole moment, propensity of ethyl-ethyl association, etc) of the ethanol-water binary mixture also show irregularities around xEtOH = 0.10-0.15. We have also discovered that the hydrogen bonding pattern of ethanol rather than water reveals a change in trend near the similar composition range. As the anomalous behavior of the physical/dynamical properties along with the pair hydrophobicity in an aqueous binary mixture of amphiphilic solutes is a common phenomenon, our results may provide a general viewpoint on these aspects.