GI have notice kids crossing with the left hand. There is, of course, among humans, a bias toward right-handedness because most humans are right-handed. Dignity has always been accorded to the right hand in culture and religion, our own not exempted. Revelation follows this bias, the right-hand being the place of honor. The left hand has through the ages come under opprobrium. In Latin the left is “sinister” from which we have our word sinister, meaning under-handed, evil. In Utah many years ago at daily Mass a priest blessed with his left hand. I asked this odd man why? He said what difference does it make, either right or left is equally good. He is right in one sense but because of the use in Revelation of the right hand as honorable and the practice for millennia, it is not kosher to use the left in ceremony/liturgy. The left is associated with the occult and satanic ritual and so is symbolically laden. On the other hand, if the left is all you can use, priest or lay, it’s fine.