Why are some people right-handed, and others are left-handers?
In nature randoms does not happen. Each feature of the structure and life activity of any organism is the result of a long evolutionary process, which is influenced by internal (genetic) and external (environmental) factors. But before talking about a person, I would like to see that right-handed and left-handers are in the animal world.
For example, among mice is about the same number of right-handers, left-handers and ambidexters (those who are not inherent is not inherent in the allocation of the lead limb). In populations of cats may prevail right-handers or left-handers, but ambidexters less. Among the wild chimpanzee left twice the right hand, and the ambidexters are rare. At the same time, in captivity most primates – right-handers. Maybe the main reason for their "rights" is the learning process and imitation of person?
What paw mouse for the first time successfully completed the task, that it will be used in the future
Genetics plays a considerable role, but not everything depends on it. So, the mice inherit the stability of the leading limb selection skill, but the selection itself is case: which mouse for the first time successfully completed the task, that it will be used in the future. Primates are not so easy. In the process of evolution, they captured more complex skills than the same mice. Therefore, the separation of functions between the hemispheres of the brain demanded a clearer genetic consolidation. Even with a random choice of lead limb, like mice, its further fixing or a change depends on external factors, especially the training of the offspring of instrument activities. In particular, from the preference of the author of the gun or just experience of senior. Already the simplest primitive guns – Olduva pebbles – mostly intended for use with their right hand. Thus, right-handed and ambidexters received an advantage over left-handers who had to be repaid.
What hand will be the lead, is determined already during the intrauterine development, or rather, in the first trimester of pregnancy. If the mother is experiencing stress, it may turn out that the child will become leading left hemisphere and left hand. In addition to stress it may affect ecology.

Moreover, the "handa" must be determined precisely with respect to the dominant hemisphere. In fact, left-handers are people who have dominant hemisphere and hand are on one side of the body, left, and not those who have learned to use the left hand for any reason. By the way, due to the fact that the left-handers constantly have to invent their ways to master the world, they are considered more creative. But the statistical analysis of the frequencies of the combinations of a half-condition and "manual" shows that the left- and the rights are changing unsystematicly, that is, there is no obvious evolutionary role.
The development of humanity led to the emergence of conventions in society. People who differ from the rest often became objects for ridicule, and sometimes even suspected due to the unclean force. For example, Peter I issued a decree, according to which left-handers could not be considered witnesses in court (about his ambiguous decrees "My Planet" prepared a test – check how well you know how to distinguish reality from fiction). Red, left-handed and criminals did not allow communion, not allowed to church. In many sacred books it is written that Levcy – from the devil.
In the Soviet Union, the disapproval of leftovers was manifested in active reappearness. Due to the preservation of the genetic diversity of left-handers continue to be born now, approximately 15% of cases. Most often they meet among men. True, this pattern is characteristic only for countries with still severe gender inequality. For example, in Sweden, Norway and Finland, where the influence of gender stereotypes is least pronounced, left-handers are found equally often both among men and among women.