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It is well established that the ground-state electron configuration of the octahedral Co^{3+} ion is t_{2g}^{6}e_{g}^{0}, which corresponds to a low-spin (LS) state. However, we theoretically demonstrate that the octahedral Co^{3+} ion in Co_{3}S_{4} prefers a high-spin (HS) state with the t_{2g}^{4}e_{g}^{2} configuration, resulting in unusual magnetism. The density-functional theory plus U calculation and ligand-field theory show that weak crystal-field splitting associated with S^{2−} induces a spin crossover from the LS to HS state of the octahedral Co^{3+} ion along with a weak Jahn-Teller-like elongation, and as a result, a ferromagnetic (FM) metal phase is energetically stabilized. Nevertheless, this phase is significantly more stable than the antiferromagnetic (AFM) phase experimentally reported at low temperature. Furthermore, phonon calculations suggest that the FM metal phase is possibly one of the Co_{3}S_{4} polymorphs, appearing in the certain experimental growth environment, but it is not expected to appear due to a temperature-dependent transition from the AFM phase. In addition, the Lyons, Kaplan, Dwight, and Menyuk theory shows that this phase is further expected to undergo a phase transition to the frustrated magnetic state. We believe that our work provides insight into magnetism of cobalt compounds and also paves the way to achieve the HS Co^{3+} by design.