Dancing is not a form of expression for the Christian liturgy. In about the third century, there was an attempt in certain Gnostic-Docetic circles to introduce it into the liturgy. For these people, the Crucifixion was only an appearance. Before the Passion, Christ had abandoned the body that in any case he had never really assumed. Dancing could take the place of the liturgy of the Cross, because, after all, the Cross was only an appearance. The cultic dances of the different religions have different purposes - incantation, imitative magic, mystical ecstasy - none of which is compatible with the essential purpose of the liturgy of the “reasonable sacrifice”.
Commentary: Many unsuspecting Catholics, clergy included, are so unaware of the history - and in this case, the liturgical history - of the Catholic Church that they see prohibitions, such as that of the "liturgical dance", as unjust curtailment of liturgical expression. The Holy Father explains that there is a background against which this prohibition is to be understood. Further to that, this prohibition has to also be understood in the light of the universal religious practices common to mankind.
The liturgy, although being a celebration, is also a sacrifice, and as such is nothing to dance about. Dancing and all sorts of popular frenzies are not the ways in which the sacrifice should be celebrated and commemorated. The gravity of Christ's one true sacrifice must evoke the deepest sense of awe and dignified reverence of the people before "the Lamb of God who takes away the sins of the world".
Any kind of singing, posture or action that threatens to detract our literal attention from the cross of Christ must remain alien to the liturgical senses of the Church. For this reason, dancing (and for that matter, jumping and waving one's hands in the air as one would in an open-air pop concert) is alien to the liturgical tradition of the Church.
To know history is to be Catholic; to remain ignorant of history is to be heretic.