The answer
It is just a matter of local tradition. In our eastern mentality, the left is considered the place of darkness and dishonour, and the right is the place of honour and righteousness. So when we make the sign of the cross we are being taken from the place of dishonour to the place of honour. In Greek tradition, the right is considered distant from the heart and the left is the place close to the heart, so when the Greeks make the sign of the cross, they are being taken from the place far from God, to the place close to God, and thereby they ask the Holy Spirit to come and dwell within them. It makes no difference either way because in both situations, we are asking the Holy Spirit to dwell within us and strengthen us.
H.G. Bishop Moussa