It has been accepted from about 1980 that there is lateral specialization of brain usage for humans, and it has more recently come to light that a lateral division of labor also takes place in the brains of other animals. However; during that time there has been no universally successful general model of cognitive lateralization. Instead, we have a topical landscape where there is no clear consensus, various models are cited in support of different research results, and there have been few comparative reviews of the available models as the topic has become too broad. This paper suggests a unifying principle that accounts for many aspects of lateral specialization in the brain, and offers tools to help develop a better general model of lateralization. Simply put; the two halves of the brain appear to address opposite phases of directional processes. While the left brain can take things apart and separate or distinguish the individual pieces, the right brain appears better at assembling those pieces, seeing how they fit together, and making them function as a congruent whole. But this same metaphor extends to a wide range of transformations which are directional and/or reversible. The key element, which makes this idea universal, is that many events in life are irreversibly directional, as they are tied to the ongoing flow of time. That is; time itself is a directional process which compels all creatures to move forward, in terms of our own evolution in time. This explains why even relatively primitive creatures develop brains that are laterally specialized.