Left handed people are at slightly increased risk of a long list of diseases and disabilities, and so the question is why left handed people still exist as about 10% of the population. The Forey Raymond hypothesis stated that those who were left-handed had one advantage which outweighed these negatives; they were better at fighting. When confronted with a south paw one has to change the way they defend and attack. Unfortunately the proportion of left-handedness has not been shown to correlate strongly with the level of violence in a society. A riffing theory posited that we know left handed people are over-represented in sports, and so perhaps athletes have a higher number of children.
An entirely alternative explanation does away with all of this and focuses on the hemispheres of the brain. As language and motor control was evolutionary selected for this emphasis on the left hemisphere in the brain also brought about a preference for right handedness (left maps to right). That means that either left handers will decrease in number over the next many millennia, or in a game theoretic sense they will exist as around 1/10th of the population because within an environment of majority right handers the left handers prosper and counterbalance their deficiencies.