A possible reason why left-handedness is rare but not extinct:
“It is hard to box against a southpaw, as Apollo Creed found out when he fought Rocky Balboa in the first of an interminable series of movies. While “Rocky” is fiction, the strategic advantage of being left-handed in a fight is very real, simply because most right-handed people have little experience of fighting left-handers, but not vice versa. And the same competitive advantage is enjoyed by left-handers in other sports, such as tennis and cricket.
The orthodox view of human handedness is that it is connected to the bilateral specialisation of the brain that has concentrated language-processing functions on the left side of that organ. Because, long ago in the evolutionary past, an ancestor of humans (and all other vertebrate animals) underwent a contortion that twisted its head around 180° relative to its body, the left side of the brain controls the right side of the body, and vice versa. In humans, the left brain (and thus the right body) is usually dominant. And on average, left-handers are smaller and lighter than right-handers. That should put them at an evolutionary disadvantage. Sporting advantage notwithstanding, therefore, the existence of left-handedness poses a problem for biologists. But Charlotte Faurie and Michel Raymond, of the University of Montpellier II, in France, think they know the answer. As they report in the Proceedings of the Royal Society, there is a clue in the advantage seen in boxing.”
More here from The Economist.