The idea that allometry in the context of brain evolution mainly result from constraints channelling the scaling of brain components is deeply embedded in the field of comparative neurobiology. Constraints, however, only prevent or limit changes, and cannot explain why these changes happen in the first place. In fact, considering allometry as a lack of change may be one of the reasons why, after more than a century of research, there is still no satisfactory explanatory framework for the understanding of species differences in brain size and composition in mammals. The present paper attempts to tackle this issue by adopting an adaptationist approach to examine the factors behind the evolution of brain components. In particular, the model presented here aims to explain the presence of patterns of covariation among brain components found within major taxa, and the differences between taxa. The key determinant of these patterns of covariation within a taxon-cerebrotype (groups of species whose brains present a number of similarities at the physiological and anatomical levels) seems to be the presence of taxon-specific patterns of selection pressures targeting the functional and structural properties of neural components or systems. Species within a taxon share most of the selection pressures, but their levels scale with a number of factors that are often related to body size. The size and composition of neural systems respond to these selection pressures via a number of evolutionary scenarios, which are discussed here. Adaptation, rather than, as generally assumed, developmental or functional constraints, thus appears to be the main factor behind the allometric scaling of brain components. The fact that the selection pressures acting on the size of brain components form a pattern that is specific to each taxon accounts for the peculiar relationship between body size, brain size and composition, and behavioural capabilities characterizing each taxon. While it is important to avoid repeating the errors of the “Panglossian paradigm”, the elements presented here suggests that an adaptationist approach may shed a new light on the factors underlying, and the functional consequences of, species differences in brain size and composition.