The magnetic bistability present in some molecule-based magnets is investigated theoretically at the microscopic level using the purely organic system TTTA (1,3,5-trithia-2,4,6-triazapentalenyl). The TTTA crystal is selected for being one of the best-studied molecule-based systems presenting magnetic bistability. The magnetic properties of the high- and low-temperature structures (HT and LT phases, respectively) are accurately characterized by performing a First-Principles Bottom-Up study of each phase. The changes that the magnetic exchange coupling constants (J(AB)) undergo when the temperature is raised (LT -> HT) or lowered (HT -> LT) are also fully explored in order to unravel the reasons behind the presence of these two different pathways. The triclinic LT phase is diamagnetic due to the fact that the nearly eclipsed pi dimer is effectively magnetically silent and not to formation of a covalent bond between two TTTA molecules. It is also shown that bistability in TTTA results from the coexistence of the monoclinic HT and triclinic LT phases in the temperature range studied.