Cases where a catalyst becomes more active and potentially more selective, due either to modifications of a precatalyst or by interaction with the reaction product, do not obey the Frank model. In these reactions, because the total active catalyst concentration is necessarily limited by that of the catalyst originally employed, the asymptotic approach to homochirality predicted by the Frank model cannot occur. Observation of sigmoidal behavior is insufficient to support the a) authentic autocatalysis proposal of an authentic autocatalytic reaction in the sense of the Frank model. By contrast, in an authentic, truly self-replicating autocatalytic reaction that is continually fed with reactants, catalyst concentration may increase indefinitely, allowing for both an accelerating rate and a continually improving product selectivity that asymptotically approaches homochirality. Thus, one key to the search for a chemical system from which homochirality can emerge is a decisive distinction between these other kinetic behaviors, which may be classified as autoinductive catalysis and will not lead to homochirality, and true self-replicative autocatalysis, which potentially may lead to homochirality.