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.
I used to be extremely left hand dominant and would pretty much do everything, including shaking people's hands, with my left hand. (until the day I broke my middle finger on my left hand; then I had to learn how to use my right hand)
Haha, I was the other way, tbh. I started out right-hand dominant, but I broke my right arm when I was young and had to use my left hand for 8 weeks. After that I was able to use both equally. The right hand is still more comfortable for me, but for other people it's almost impossible to tell.
Anyone who fences will have done this multiple times, the're holding a sword in their right. except lefthanders, then you do this awkward left to right grip where one person has to turn their hand over.
I'm left-handed, so doing this is always fun. Even more, it's always fun to ask right-handed people to consider doing things left-handed, because then they get all freaked out at the number of stuff they don't realize they naturally do right-handed & have to do with their left.
There are reasons why people shake with their right hands, and it isn't just because most of us are right handed. Think medieval pre-toilet paper times. I'm sure the answer will come, just give it time.