In almost all of the magickal traditions I've worked with, the right side is active/projective while the left is passive/receptive. I always assumed this was due to the majority of people being right-handed - I even tried early on in my studies to swap them in my personal practice to fit my being left-handed, but it never felt quite right.
Last night, though, I discovered that apparently most people are better at tactile discrimination with their left hands, due to the natural specialization of the hemispheres of the brain (hence the effect is stronger in males than in females). Unfortunately the study cited only used right-handers, so I can't tell if it truly is independent of handedness.
And it makes sense that the side better able to process tactile input would become associated with receptivity.
(The book I got this from is "What's Going on in There? How the Brain and Mind Develop in the First Five Years of Life" by Lise Eliot, which is absolutely fascinating.)