Development of Mg-ion batteries as advanced electrochemical energy storage systems relies on the design and discovery of high-voltage positive electrode (cathode) materials. To date, a variety of sulfide cathodes have been reported (e.g., MgxMo6S8, MgxTi2S4, etc.), but the voltages of these materials are too low to prepare a high energy density Mg cell. Theoretical computations predicted that MgxCr2S4 operating with the high-voltage Cr3+/4+ redox couple would serve as a suitable cathode candidate, but experimental attempts to extract Mg2+ from the lattice have been largely unsuccessful. We show that reversible electrochemical activity within a thiospinel framework (AB2S4) relies on a redox-active transition metal present in the B site; otherwise, anionic redox activity triggers decomposition of the spinel structure. Since Cr and S states are highly coupled in MgCr2S4, the Cr3+/4+ redox couple is inaccessible so that reversible (de)intercalation of Mg2+ cannot occur and charging leads to dissolution of the active material. These findings point to an insufficiency in the screening criteria previously used to identify MgCr2S4 as a promising Mg cathode. Thus, a computable descriptor based on the electronic structure of the discharged material is proposed to predict the prevalence of cation vs anion redox and improve future surveys of potential candidates. It is unlikely that the high-voltage Cr redox couple will be accessible to oxidation in the presence of sulfur within the restrictions of a spinel framework; however, it is possible that a suitable layered MgxCrS2 structure could serve as a reversible high-voltage Mg cathode.