Interestingly Stone Age implements discovered seem equally divided between left and right and studies of cave drawings have indicated a preference for the left hand. It is only when tools became more sophisticated that a clear hand preference emerged. The right hand preference may have originated in sun worship.
In the Northern hemisphere you have to face south to follow the sun and move from left to right until the suns sets in the west. This gave moving to the right and the right hand side a great significance. Another theory says that as the heart is on the left hand side, a shield would have to be in the left hand to defend it and any weapon therefore had to be held in the right, which became the dominant hand.
Ah who knows if these theories are true but today is our day in the sun.