Genetics is the answer:
Clare Porac, a professor of psychology at Pennsylvania State University who studies handedness, explains.
Researchers who study human hand preference agree that the side of the preferred hand (right versus left) is produced by biological and, most likely, genetic causes. The two most widely published genetic theories of human hand preference argue that evolutionary natural selection produced a majority of individuals with speech and language control in the left hemisphere of the brain. Because the left hemisphere also controls the movements of the right hand--and notably the movements needed to produce written language--millennia of evolutionary development resulted in a population of humans that is biased genetically toward individuals with left hemisphere speech/language and right-hand preference. Approximately 85 percent of people are right-handed. These theories also try to explain the persistent and continuing presence of a left-handed minority (about 15 percent of humans).
The genetic proposal to explain hand preference states that there are two alleles, or two manifestations of a gene at the same genetic location, that are associated with handedness. One of these alleles is a D gene (for dextral, meaning right) and the other allele is a C gene (for chance). The D gene is more frequent in the population and is more likely to occur as part of the genetic heritage of an individual. It is the D gene that promotes right-hand preference in the majority of humans. The C gene is less likely to occur within the gene pool, but when it is present, the hand preference of the individual with the C gene is determined randomly. Individuals with the C gene will have a 50 percent chance of being right-handed and a 50 percent chance of being left-handed.
These theories of hand preference causation are intriguing because they can account for the fact that the side of hand preference of individuals with the C gene (most left-handers and some right-handers) can be influenced by external cultural and societal pressures, a phenomenon that researchers have documented. These theories can also explain the presence of right-handed children in families with left-handed parents and the presence of left-handed children in families with right-handed parents. If the familial genetic pool contains C genes, then hand preference becomes amenable to chance influences, including the pressures of familial training and other environmental interventions that favor the use of one hand over the other. The proposed genetic locus that determines hand preference contains an allele from each parent, and the various possible genetic combinations are DD individuals who are strongly right-handed, DC individuals who are also mostly right-handed, and CC individuals who are either right-handed or left-handed. These genetic combinations leave us with an overwhelming majority of human right-handers and a small, but persistently occurring, minority of left-handers.*