In networks with a minority and a majority community, it is well-studied that minorities are under-represented at the top of the social hierarchy. However, researchers are less clear about the representation of minorities from the lower levels of the hierarchy, where other disadvantages or vulnerabilities may exist. We offer a more complete picture of social disparities at each social level with empirical evidence that the minority representation exhibits two opposite phases: at the higher rungs of the social ladder, the representation of the minority community decreases; but, lower in the ladder, which is more populous, as you ascend, the representation of the minority community improves. We refer to this opposing phenomenon between the upper-level and lower-level as the \emph{chasm effect}. Previous models of network growth with homophily fail to detect and explain the presence of this chasm effect. We analyze the interactions among a few well-observed network-growing mechanisms with a simple model to reveal the sufficient and necessary conditions for both phases in the chasm effect to occur. By generalizing the simple model naturally, we present a complete bi-affiliation bipartite network-growth model that could successfully capture disparities at all social levels and reproduce real social networks. Finally, we illustrate that addressing the chasm effect can create fairer systems with two applications in advertisement and fact-checks, thereby demonstrating the potential impact of the chasm effect on the future research of minority-majority disparities and fair algorithms.