The question of whether you are right or left handed relates to language dominance. So says psychologist Professor Chris McManus of University College, London who has authored several papers on the subject. Most people use the left half of their brain for language processing and it so happens that the left hand side of the brain controls the right hand side of the body. This means that the dominant hand is controlled by the side of the brain responsible for language. Professor McManus says yes.
Humans are almost unique in using language and are almost unique in having a handedness bias.
The change probably occurred between two and four million years ago with a genetic mutation that granted the left hand side of the brain the ability to process at much higher temporal resolution. This allows much finer co-ordination of the lips and tongue as well as allowing rapidly changing information from our ears to be interpreted quickly enough. It also increases the dexterity of the fingers of the right hand however and this would tend to favour the use of that hand over the left. The interesting question about left-handedness is therefore not why it is so rare, but why it persists in the population at all. Rare mutations normally become fixed in the gene pool or else are eliminated altogether but the incidence of left-handedness appears to have been constant for at least five thousand years and perhaps for as much as fifty thousand.