As a convert I always accepted this practice as a normal part of the Mass, but once I attended the Latin Mass, realized it was not; and that is part of the reason I prefer the Latin Old Mass over the vernacular New Mass.

The sign of peace breaks up the contemplative, reflective posture so important to Mass, something this article from Crisis Magazine notes.

An excerpt.

At the request of Pope Emeritus Benedict XVI, a requisite inquiry into the timely appropriateness of the Latin Rite’s gesture of peace shared amongst the people during the Holy Sacrifice of the Mass commenced almost a decade ago. The Vatican’s Congregation for Divine Worship and the Discipline of the Sacraments (“the Congregation”), under the papal authority of a new Holy Father, Francis, disseminated publicly this year their conclusions on the placement of the gesture. In its Circular Letter on the Ritual Expression of the Gift of Peace at Mass, the Congregation, although reiterating authoritative instruction on the avoidance of gestural abuses, decided that the gesture shall remain in the current liturgical place.

It is indeed born of a sound theology that amongst the faithful there is some sign of peace during the Mass, which in the current Novus Ordo Missae (contemporary Ordinary Mass) occurs prior to the breaking of the consecrated body and soon before Catholics of good conscience are invited to consume the actual flesh and blood of God. Further, the gesture also correlates with doctrinal teaching on communal worship and Christian fraternity.

Benedict XVI’s request for study of the topic, however, brings papal credence to the idea that the placement of the gesture is thoroughly and unreasonably anachronistic. Quoth Benedict XVI 2007 post-synodal apostolic exhortation Sacramentum Caritatis:

Taking into account ancient and venerable customs and the wishes expressed by the Synod Fathers, I have asked the competent curial offices to study the possibility of moving the sign of peace to another place, such as before the presentation of the gifts at the altar.

Indeed, it is the place of the peace gesture in the Novus Ordo Missae that is the problem.

Rather than reminding the faithful that they are sharing in a solemn sacrifice and preparing to participate communally in worship (lex orandi), and in the Supper of the Lord, receiving His very body and blood as did the apostles on the night that they were told He was to become the Passover Paschal Lamb, the gesture of peace in its current place obliterates the reverence of the moment.

As Saint John Paul II reminded the faithful in his encyclical letter Ecclesia De Eucharistia: “Every priest who celebrates Holy Mass, together with the Christian community which takes part in it, is led back in spirit to that place and that hour.” By “that hour,” John Paul II meant “the hour of his Cross and glorification.”

If at “that hour” Mary and John on Calvary looked up to the cross, smiled, hugged, and shook hands, this column would have nary any authority; but, alas, the Gospel of John says Mary and John did nothing of the sort.

The mind and soul are to be fixed upon the transsubstantiatio (“transubstantiation”) occurring on the altar; thus one is to be focused in soul, mind, and body, solely upon God.

The anachronistic confraternal peace gesture takes the soul, mind, and body away from the necessary contemplative prayer, thought, and internal preparation in which one should be engaged immediately prior to the receipt of Holy Communion. In a few short liturgical seconds, one is re-directed from the rightful focus on Christ and the Father (the latter most directly through the recitation of Jesus’ own Pater Noster [“Our Father”]), and onto the people by way of the peace gesture. The liturgy then swiftly reverts focus back onto the Lord with the chanting of the Agnus Dei (“Lamb of God”), which repeats twice the request of the faithful for the Lord to “have mercy on us,” which is surely aidful in, and companion to, a proper examination of conscience and soul in preparation for unworthy receipt of Holy Communion. One need not have considerable knowledge of the liturgy to see that the peace gesture just does not fit.

Retrieved December 29, 2014 from http://www.crisismagazine.com/2014/vaticans-sign-peace-liturgical-placement-affirmation-missed-opportunity-reclamation-reverential-mass