Children should play chess because chess can impart valuable life skills and experiences to it’s players. There has been extensive scientific documentation that chess quantifiably improves memory, critical thinking, mathematics, and reading skills (to name a few). The earlier a child begins learning and playing chess, the greater the likelihood that he/she will excel in the aforementioned areas. The concept of plasticity of the developing cerebral cortex in children suggests that the earlier a child begins learning a skill/language/etc.. – the more natural success he/she will experience as the developing brain is very similar to an extremely effective sponge (especially in the earlier stages). A good example is that children are much better at learning languages at an early age – because their brain is naturally more receptive to encoding external stimuli into meaningful patterns. The following article by Mary Alward (with reference to original material by Chess Coach Grandmaster Yasser Seirawan) details the benefits of teaching chess to children.
Introduction by William Stewart from OnlineChessLessons.net