Colin Donovan, VP of Apologetics for EWTN, explains it here:
Among the laity this practice began with the charismatic renewal. Used in private prayer it has worked its way into the Liturgy. It is a legitimate gesture to use when praying, as history shows, however, it is a private gesture when used in the Mass and in some cases conflicts with the system of signs which the rubrics are intended to protect. The Mass is not a private or merely human ceremony. The symbology of the actions, including such gestures, is definite and precise, and reflects the sacramental character of the Church’s prayer. As the Holy See has recently pointed out, confusion has entered the Church about the hierarchical nature of her worship, and this gesture certainly contributes to that confusion when it conflicts with the ordered sign language of the Mass.
As has been pointed out by clergy on CAF in many past threads, the GIRM (to be redundant, Roman Rite) prohibits laity from bringing innovations into the liturgy when the rubrics are silent about those, regardless of what was done in temple worship in ancient Judaism, and what was or is done in any Eastern Rite. This interpretation is from several different members of the clergy, in different dioceses, over the last 6 years. They would know way better than any lay person here, how to interpret the General Instructions.
In any case, I find it extremely distracting when people do this. Also, I have never seen it done (in my own many experiences) in any way except to draw attention to the person engaging in it. It’s as if people need their own theater at Mass. I remember fairly recently at a liturgical celebration which drew more people than usual, a couple of women on either side of me used the occasion to practically engage in their own public hand-dance – with elaborate hand gestures. And the weird thing was, they were not even facing the altar, like the rest of us! Rather, they were tilting their body to the side, semi-facing the congregation! Talk about wanting an audience. Not to be distracted by it would have required me to keep my eyes closed during the entire Mass.
The theater is the altar. The protagonist of the event is Jesus Christ himself, with the narrator being the priest. And the priest, using the Orans position, acts on our behalf. He doesn’t need our “help.”
I can understand people doing this at a charismatic Mass, not a traditional Sunday Mass, whether NO or EF or whatever. Because, as Colin points out in the rest of the article, the Roman liturgy strives for unity and for representation by the ministerial priesthood, with the congregation participating by silent assent and voiced assent, not with some people doing some gestures, other people doing other random gestures, and another group reserved and uncomfortable.
At Protestant services, there is nothing particularly sacred going on in the sanctuary, in that there’s no sacrifice being remembered, no Real Presence being realized, etc. Generally, it’s about the preaching from the pulpit or sanctuary area, sometimes a choir facing the congregation from that location, and the solemnity which characterizes Roman Catholic celebrations is absent. There may be fervor and much else that is laudable, and a great deal of fellowship and unity, but it is a different expression of unity than what occurs in the Roman Rite. And at such services there is often a great deal (usually unanimous) hand-waving or hand-raising, and a great deal of emotion expressed. Valid for those communities, those are nevertheless celebrations of an entirely different character than what a lay Catholic should be able to expect as distinctly and profoundly different from that.