To be honest I'm not entirely sure. They gave us some story about allies meeting without shields (which would be held in the left hand as most people are right-handed and would naturally have their weapons in their dominant hands) but I have no idea how accurate that was.
We shake with our right because back before there was toilet paper our ancestors used the left hand to wipe their asses after they took a crap XD
I once tried to shake hands with my left hand with a boy who was new to my school and foreign to America but couldn't speak English and he just looked very confused and stared at my left hand before saying something I couldn't understand and walked away.... I think he cussed me out.... XD
I do this ALL the time without noticing, because I'm ambidextrous, and some things I just use my left hand for. People always go to shake my hand and then stare blankly, not able to figure out why it isn't working out right.