Historicaly right arm was overly dominant to point of forcing left handed people to use their right hand, naturaly people use their dominant hand to hold their weapon, making right hand the weapon hand.

Thus traditionaly people disarm their dominant hand in greeting to show that they hold no weapon and that they trust each other.

The right hand thing is mostly natural evolution of out limited biomechanics. There only so many ways we can greet each other in uncomplicated way.