Y'know how people in many parishes can't seem to keep their hands to themselves during the Our Father?
In many parishes they get grabby and, though in American culture holding hands with another person is a gesture of intimacy (sweethearts do it, spouses do it, parents and children do it, complete strangers do not do it), suddenly the person next to you wants to engage in the gesture with you, a complete stranger.
In my own case, I solve this problem by clasping my hands in front of me and closing my eyes. 99.99% of the time that takes care of the issue, though I did once experience an elderly woman using her fingers to pluck at my elbow in an attempt to pierce through my obviously meditative attitude and get me to Conform to the handholding she wanted to inflict on me.
Needless to say, a lot of folks find this (unauthorized) grabbiness disturbing, and there has been perplexity at the episcopal level concerning what to do about it.
In come some helpful liturgists, who have suggested that instead of holding hands, people imitate the priest, who happens to be in the orans position at this moment, with his hands outstretched in prayer.
This has the advantage of not automatically inflicting hand-to-hand contact on the people next to one in the pew, though in an especially crowded pew it is not a sure recipe for avoiding all bodily contact. (One may experience a whack to the face, or at least the uncomfortable experience of becoming visually acquainted with the back of a stranger's hand better than you know your own.)
One detects in the liturgists' suggestion a further motive besides avoiding excessive touchy-feeliness (particularly since liturgists have themselves been excessively touchy-feely in recent years). Could it be . . . a desire to get the laity to imitate the priest and thus further blur the lines between the two?
"Oh, surely not!" you're saying. "Liturgical planners have been scrupulous since the reform of the liturgy about making sure the roles of priest and laity are at all times clearly distinguished. Just ask them! They'll tell you!"
However that may be, the Holy See has been concerned about the laity unduly aping the priest at Mass, and in the 1997 Instruction on Collaboration, an unprecedented conjunction of Vatican dicasteries wrote:
6 § 2. To promote the proper identity (of various roles) in this area, those abuses which are contrary to the provisions of canon 907 [i.e., "In the celebration of the Eucharist, deacons and lay persons are not permitted to say the prayers, especially the eucharistic prayer, nor to perform the actions which are proper to the celebrating priest."] are to be eradicated. In eucharistic celebrations deacons and non-ordained members of the faithful may not pronounce prayers — e.g. especially the eucharistic prayer, with its concluding doxology — or any other parts of the liturgy reserved to the celebrant priest. Neither may deacons or non-ordained members of the faithful use gestures or actions which are proper to the same priest celebrant. It is a grave abuse for any member of the non-ordained faithful to "quasi preside" at the Mass while leaving only that minimal participation to the priest which is necessary to secure validity.
This instruction, incidentally, was approved by John Paul II in forma specifica, meaning that the pope invested it with his own authority and is binding on us with the pope's authority and not merely the authority of the authoring congregations.
Now, what gestures are proper to the priest celebrant? The orans gesture when praying on behalf of the people is certainly one of them. The priest celebrant and no others (not even concelebrating priests) are directed to make this gesture in the rubrics.
In some places, some laity may spread their arms whenever the priest spreads his in a kind of "Back atcha!" motion. I've even seen some do a phenomenal pantomime of tossing an invisible ball to the priest by swooping their palms close together and then spreading them apart as they assume the orans posture. But this is clearly apart from the rubrics.
If the orans posture is one proper to the priest celebrant in the liturgy then the laity should not be imitating it.
But Ed Peters raises an interesting question:
The rubrics at present call for him to do so, so he should do so until the rubrics are changed, but given the underlying logic of the rubrics and the way the saying of the Our Father has developed in Mass, Ed raises an interesting question as to whether the rubrics might oughta be changed.