The Cattell-Horn-Carroll (CHC) taxonomy of cognitive abilities married John Horn and Raymond Cattell's Extended Gf-Gc theory with John Carroll's Three-Stratum Theory. While there are some similarities in arrangements or classifications of tasks (observed variables) within similar broad or narrow dimensions, other salient theoretical features and statistical methods used for examining and supporting them are in direct opposition. In this article, the theoretical disagreements between Carroll and Cattell-Horn and theoretical incongruencies between their models are delineated, which raises substantive challenges to CHC. Additionally, there are practical and substantial measurement obstacles that further threaten "practical" application of CHC. We conclude that the problems are due to some fundamental differences that likely will not change, so call for an annulment of this arranged but unhappy marriage.