As the 1935 Boy Scout handbook says, "By agreement of the Scout Leaders throughout the world, Boy Scouts greet Brother Scouts with a warm left hand clasp." (wikipedia
). But what's the origin of this form of greeting?
Lord Baden-Powell, founder of the Boy Scouts, claimed he learned the custom from a defeated African chieftain whom he attempted to greet in 1896 by holding out his right hand. The chieftain supposedly replied: "The men in my tribe greet the bravest with the left hand." There are different versions of this story, but I think all of them can safely be dismissed as bogus.
There's also a theory
that the scouts shake with their left hand because it's the hand closer to the heart. I also doubt this theory.
I think the real origin traces back to Baden-Powell's passion for promoting ambidexterity — and not just the ability to use either hand with equal dexterity, but to use both hands for different tasks, simultaneously.
Baden-Powell expressed some of these views in the brief introduction he wrote to John Jackson's 1905 book Ambidexterity, or, Two-handedness and two-brainedness
To train the human body completely and symmetrically, that is, to cultivate all its organs and members to their utmost capacity, in order that its functions may also attain their maximum development, is an obligation that cannot safely be ignored. This completeness and symmetry can only be secured by an equal attention to, and exercise of, both sides of the body--the right and the left; and this two-sided growth can alone be promoted and matured by educating our two hands equally, each in precisely the same way, and exactly to the same extent.
It is hardly possible to lay too much stress upon this bimanual training, or to attach too much important to the principke, because our hands -- and our arms, from which, for purposes both of argument and education, they cannot be separated -- not only constitute our chief medium of communication with the outer world, but they are likewise the pre-eminent agency by which we stamp our impress upon it...
The heavy pressure of my office work makes me wish that I had cultivated, in my youth, the useful art of writing on two different subjects at once. I get through a great deal extra -- it is true -- by using the right and left hand alternately, but I thoroughly appreciate how much more can be done by using them both together.