What an interesting question! All sorts of theories have been advanced over the years. It is only recently that we have some understanding of what makes some people right handed and others (about 5% of the population) left handed. This "understanding" is far from complete. The biggest achievement is that being left handed is no longer seen as a bad thing, something a person needs to be "cured" of.
50 years ago, a left handed child was punished for using their dominate hand, and "taught" instead to do things right - i.e. with their right hand. The school system actively encouraged it (and still does to large extent. Most desks are made for righties). Many lefties learned to write and function with their right hand. A few could not be taught to use their right hand. A few became ambidexterous. For the latter category of people, the use of both hands let them develop the musculature and ability to use both for all tasks. My father was born lefty, but became ambidexterous from having "righty" instruction at school. At home he continued to use his left hand.
Anyway, there are two sides of the brain. The left side of the brain controls the right side of the body while the right side of the brain controls the left side of the body. (It has to do with the flow of the nerves from the brain to the rest of the body. The right and left sided nerves cross over in the neck.)
Some people favor one side of the body over the other, b/c of the layout of their particular anatomy. The vast majority are more comfortable using the left side of the brain, and are thus righties. A small percentage, are more comfortable using the right side of the brain and they are lefties. (The comfort level comes from what feels right for them. In other words it's an innate feeling. As noted above, however, the innate disposition can sometimes be modified, but there is no reason to do so).
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