The implication given is that left-handers make good military leaders by virtue of their left-handedness, and the justification for such a conclusion (where one is offered) is likely to be along the lines of the acute sense of navigation, strategic planning and visualization enabled by the left-handers’ unique brain organization.
While there may (or may not) be some truth to the claim, it is a mistake to make a rule out of such anecdotal evidence and cherry-picked data. For example, just listing some famous names offers no prima facie reason to suppose that the overall numbers of left-handed military leaders are anything other than what one would expect from the left-handed proportion of the general population.
When one looks at the evidence for individual claims though (rather than just taking the word of numerous websites for granted), the issue immediately clouds still further. For example, the case for Alexander the Great being left-handed is tenuous at best. His constant inclusion at the top of lists of left-handers is a relatively recent phenomenon, apparently arising from a misreading of accounts in the 1960s and thereafter, and possibly arising from his own (entirely unsubstantiated) claim to have conquered a country of left-handed people. In fact, Alexander is always shown in classical depictions as right-handed, and none of the contemporary or near-contemporary historians, who documented his life so meticulously, make any mention of an unusual trait like left-handedness.
The notable Egyptian Pharaoh Ramses II is usually numbered among the host of left-handers, presumably on the strength of the tomb inscription in which he claims “with my left hand I hurled the dart”, totally ignoring the next line which reads “with my right I swung the blade”. Incidentally, neither does this make him ambidextrous (what is a man wielding two weapons to do?)
It is not at all clear why Julius Caesar should be considered a left-hander, as he usually is. There does not appear to be any documentary evidence to suggest it, and to assert that he encouraged the Roman practice of shaking the right hand in greeting because he was left-handed (and therefore, presumably, unscrupulous) is circular reasoning of the highest order. The common inclusion of the Roman Emperor Commodus in such lists is even more puzzling. Although almost definitely a left-hander, and a fierce and merciless fighter, Commodus was one of Rome’s worst Emperors and a poor military leader. Interestingly, Emperor Tiberius was also a left-hander according to biographer Suetonius, and a much better military leader, but he is hardly ever mentioned in the lists. All this merely demonstrates the tendency for websites and blogs to copy each other unthinkingly.
The cases for the sinistrality of several other historical leaders are equally shaky. Charlemagne, for example, is always depicted in art holding a sword in his right hand, and often an orb in his left, hardly evidence of left-handedness. English King Edward III was forced to be left-handed due to accident to his right, and it seems unlikely, especially given the period and culture in which he lived, that he would have been naturally or voluntarily left-handed. Joan of Arc has been labelled left-handed on the evidence of hand-writing analysis and from artistic depictions of her holding as sword in her left hand (although at that time witches and heretics were usually depicted as left-handed - considered by the Church to be the mark of the Devil - whether they were or not).
Napoleon Bonaparte is shown in some paintings and statues holding his sword with his left hand and in others with his right, and citing his habit of marching his troops on the right-hand side of the road (also see the section on Handedness and Road Use) as “proof” of his left-handedness is merely more circular reasoning. Other members of these lists, such as King Louis XVI of France, Simón Bolívar and Otto von Bismarck, were certainly high-handed, but there is little or no evidence to suggest that they were left-handed, and it is not at all clear where such “facts” have come from. Fidel Castro is widely believed to have been a left-hander, possibly due to an equally mysterious and unfounded myth that he once tried out as a left-handed relief pitcher for an American major league baseball team in the 1940s (or perhaps just due his brand of politics).