Fr. Anthony Nelson posted the following remarks to the Orthodox Email Forum (Indiana List) in reply to the following question: Has anyone on this list got a definitive answer on why Orthodox and Roman Catholics do the sign of the cross on themselves in the oppostie manner?
Answer: The sign of the cross of the Byzantines is different from that of the Latins. The thumb and first two fingers of the right hand are joined at the tips; the fourth and fifth fingers are folded over the palm. The two fingers and thumb signify the three Divine Persons of the Trinity, while the other two fingers symbolize the two natures in Jesus Christ. With the fingers so joined, the forehead is touched first (" In the name of the Father"), then the breast ("and of the Son"), the right shoulder ("and of the Holy..."), and finally the left shoulder ("Spirit. Amen. "). Meanwhile, the head and shoulders are slightly bowed as a sign of submission to the Godhead.
The right shoulder is touched first, not the left as in the Latin Rite. Prior to the end of the twelfth century, Christians of both East and West made the sign of the cross from the right to the left. Latin Catholics began making it with all the fingers extended, and from the left shoulder to the right, at the time of Pope Innocent III (1198-1216). Supposedly, this meant that Jesus came from the Father to earth by becoming man, then descended into the left side, i.e., into hell, by his Passion and thence into his Father's right side, by his ascension. Another explanation was that making the sign from the left, the weak side, the side of sin, to the right, the side of salvation, would symbolize the death of Christ on the cross, and our being carried by it from the left to the right side, to salvation.
The earlier, more ancient way of making the sign of the cross, as it is still done in the Byzantine Church, from the right to the left, is understood to mean that salvation passed from the Jews, who were at the right side of God (the side of honor, belonging to the chosen people) to the Gentiles, who were at his left. Touching the right shoulder first also expresses the Christian hope to be put among the righteous on the right hand of Christ, the Judge at the Final Judgment.
In the Latin Rite the priest, when imparting a blessing, still makes the sign of the cross from the right to the left.
The ancient Christians derived their idea of the right side as being the side of righteousness, the side of honor, from the Scriptures: e.g., the Queen of heaven "stood on the right hand, clothed in a vesture wrought with gold and diverse colors" (Ps. 44:10); Jesus "sitteth at the right hand of the Father" (Rom. 8:34), etc.
In general, the complete sign of the cross was and is made to acknowledge that all of our faculties (mind, heart, and soul) and all of our strength (shoulders) are being dedicated to the service of God through the cross of Christ, the sign of our redemption.