Today, we find it odd that one should even begin to consider the left hand less "good" than the right. Many of us will remember when parents and teachers would force a child to use the right hand rather than the left for writing, eating, etc. Was the right hand "better"? Maybe, it was thought so. Or was this practice due to the fact that our world was oriented to right-hand usage and one growing up left-handed would be disadvantaged?
However, there does seem to have been a belief that the right was more honourable or holy. We used to read the Gospel from the right side of the altar because that was the place of honour and the Epistle from the left, the lesser side. In Matthew's parable of the last judgment, the sheep who are going to heaven with Jesus are on his right and the goats going to hell are on his left. Jesus risen from the dead is seated at the right hand of the Father.
Are these examples telling us that the right hand is better or that the left is "bad" or "evil"? Do you think that God created one hand good and one evil? I don't think so. And if it is humans who make one hand evil by what they do with it, then it would be the right hand for most of us since most of our tasks are performed by that hand. And right-handed people use that hand for "less honourable" tasks, as do left-handed people.
So no matter how you cut it, one hand can't be better or holier than the other.
Then, why did we make it sound as if the right was more honourable? I believe that we were simply using commonly understood symbols to convey something much more profound than which side is "better."
After all, symbols speak louder than words.
At the Last Supper, we are told, Jesus broke the bread and passed it to his disciples so he probably used both hands. I did extensive research in early and medieval Church, pre- and post-Vatican II documents, as well as in the most recent papal document but I can find no evidence as to which hand is to be used to give Communion.
Of course, it was usually the right since most people were/are right-handed. However, in Pope John Paul's recent televised Mass, a priest was clearly seen giving the Communion host to many people with his left hand.
Although fourth century St. Cyril of Jerusalem did not seem to have written how to give Communion, he does indicate how Communion is to be received: "When you approach, do not put forth the flat hand nor spread your fingers apart, but make your left hand a kind of throne for the right in which to receive Jesus. Receive the Body of Christ in the hollow of your hand, saying Amen."
He does not say whether the Body of Christ should be picked up with the left to put in the mouth or brought to the mouth with the right. The latter would be awkward and certainly more so today with the small flat hosts we use.
Therefore, they probably picked up the sacred species with the left and brought it to the mouth. Today, it is suggested that we cup the left into the right hand to receive the host, pick up the host with our right hand to bring it to the mouth.