Raising hands in prayer is a very ancient practice, and following this practice in private prayer is certainly acceptable. However, even among the clergy, only the presiding clergyman raises his hands at various points in the Liturgy. The other priests do not. The deacons raise only one hand at these points, but never both.
Why is this? I don’t recall ever reading an explanation, but I would give one answer I am certain of, and another that I think is probably true:
1. This is not the practice we have received.
2. The liturgical logic at work seems to me to be that the person who is leading the people in prayer raises his hands on behalf of all the people, and so the people, deferring to that priest or bishop, do not attempt to usurp his role, but allow him to do this alone. On the other hand, in private prayers, you are the one presiding, so to speak, and so in this case you can raise your own hands in prayer.
There is an Old Rite practice of people raising both hands when they are censed during the services, but this is a different practice. This is not done at the times when the presiding priest or bishop raises his hands.
It is important that we conduct ourselves in the services in a way that does not draw attention to ourselves, and so adhering to the practice we have received is very important. It helps everyone focus on God in prayer. The services are where we serve God in prayer and worship — not where we are served, and get to do whatever pleases us.
St. Paul admonished the Corinthians by saying: “Let all things be done decently and in order” (1 Corinthians 14:40), Commenting on this verse, St. John Chrysostom says:
“Nothing builds up as much as good order, peace and love, just as nothing is more destructive than their opposites. It is not only in spiritual affairs but in everything that one may observe this” (Homily 37:4 on 1 Corinthians).