Our Office of Divine Worship explains why the faithful should refrain from extending their hands during the Our Father at Mass:
"Further, the Second Vatican Council’s Constitution on Sacred Liturgy, Sacrosanctum Concilium, states that “no other person, even if he be a priest, may add, remove, or change anything in the liturgy on his own authority.” (SC 22.3) Since the GIRM is very specific that the priest is instructed by the GIRM (152) to extend his hands when he prays the Lord’s Prayer, for the deacons or the laity to extend their hands would be adding to the liturgy. Therefore, the practice of the lay faithful extending their hands (or holding hands) during the Our Father should not be done."
Read more:
archdpdx.org/news/divine-wor…