In most people, the left hemisphere of the brain is largely responsible for language processing and for speaking (which is an activity that employs many fine motor skills, involving the mouth, tongue, etc). The left hemisphere of the brain is also responsible for coordinating the movement and motor skills of the right side of the body, with the right hemisphere largely controlling the left side of the body. It is argued by some that it is more efficient, and requires less energy consumption, for the brain to process these two important fine motor skill functions in the same hemisphere of the brain, hence the right-hand/left-hemisphere dominance of the majority of the population. The theory also goes some way to explaining why non-humans, who lack the faculty of speech, have not developed hand dominance to anything like the same extent as humans.
This idea is supported to some extent by a 2010 French study, which showed that, when people hear spoken syllables, there is synchronized neural activity in the areas in the left hemisphere of the brain which are involved in both speech and in hand and mouth motions. There is no such synchronized activity in response to smaller units of speech (phonemes). The study authors suggest that our brains are hard-wired to process speech and language and gestures on the same side of the brain, which, for the right-handed majority of people, is the left side. This also supports the idea that speech initially arose from a combination of short sounds and hand gestures, typically made with the dominant right hand.
However, as we have seen in the section on Handedness and the Brain, although about 95% of right-handers do in fact process speech primarily in the brain's left hemisphere, it turns out that only about 19% of left-handers have right-hemisphere dominance for language function, with another 20% exhibiting bilateral language functions. Thus, well over half of left-handers also process speech in their left hemisphere and are left-brain dominant, just like right-handers, and so it appears that relatively few left-handers’ brains take advantage of this theory of efficient brain processing.
Recent developments in neuroscience indicate that the traditional right-brain/left-brain dichotomy is simplistic at best anyway, and that the brain’s connections and processes are actually much more complex (and also less hemisphere-dependent) than was previously thought. Thus, it is a gross simplification to talk of the “creative” right brain and the “logical” left brain (and thereby impute creativity to the left-hander and logic to the right-hander). Modern neurology has shown that elements of such characteristics exist in both sides of the brain, and that most tasks require the cooperation of both hemispheres. Also, the plasticity of the brain (its ability to “re-wire” its neural connections, as in the case of brain injuries, for example) is more than capable of overcoming any localized deficiency or superfluity of functionality.