The role of the ion sign in the binary H2SO4-H2O nucleation remains unclear despite significant progress in both theory and instrumentation achieved within the last decade. In order to advance the understanding of ion nucleation phenomena, a quantum-chemical study of binary sulfuric acid-water ionic clusters nucleating in the atmosphere has been carried out. We found a profound sign effect caused by the pronounced difference in the structure and properties of clusters formed over core ions of different sign. The sign preference is found to be controlled by two somewhat competing factors: hydration and sulfuric acid attachment. While hydration of cations is clearly favorable, the affinity of sulfuric acid, which largely controls the nucleation intensity, to negative ions is much higher than that to positive ions. The presence of a very large difference in the affinity of sulfuric acid between positive and negative ions suggests that nucleation of negative ions is likely favorable.