I know that no where in the Catholic Rite of Communion does it state that the communicant must make the sign of the cross after reception of the Eucharist in either species. So why is it that so many children are taught to do so in preparation of their First Eucharist?
Why do Catholics make the sign of the cross at the Eucharist?
It is an act of Catholic piety!
Before going on into the main body of my answer, I would like to point out that in the Extraordinary Form of the Mass, Communion was given in to communicants in the following way:
As the priest places a Host directly from the chalice into the mouth of each communicant, he prays for life everlasting.
Holding the Sacred Host in his right hand, the priest makes the sign of the cross with it and says:
Corpus Domini nostri Jesu Christi custodiat animam tuam in vitam aeternam. Amen.
An example of this can be seen in the YouTube video explains how a priest performs these sacred actions in very clear detail (1:42:00 and following): The Latin Mass Explained and Demonstrated for Priests.
In the Mass of Paul VI, the sign of the cross is not made by the priest at communion, unlike that of the Extraordinary Form of the Mass. And although it is not prescribed by the Church for the faithful to make the sign of the cross at communion, many do so. The laity are simply carrying on this pious tradition themselves. In the Old Rite the priest made the sign of the cross. In the New Rite, the faithful make the sign of the cross. It is a natural and organic liturgical development that should be encouraged.
Should we make the sign of the cross when we receive communion?
The rubrics don’t call for the faithful to cross themselves after receiving Communion. If a person wants to do it, as a personal act of piety, there is nothing that stops him, however.
The Church asks that we receive Communion reverently, either by slightly bowing before receiving (if we receive standing up) or by kneeling (which is always an option). Communicants should respond with “Amen” when the minister says, “The Body of Christ” or “The Blood of Christ.”
One word of caution regarding crossing oneself: It isn’t advisable to do it too quickly after receiving Communion. If a person raises his hand too quickly to cross himself, he risks striking the ciborium or chalice, which could cause an accident with the Eucharist. Before making the sign of the cross it is better for the communicant to wait a second for some distance to open up between himself and the minister. - "Ask a Priest: Should we make the sign of the cross when we receive communion?"
Many catholic make the sign of the cross at various occasions of their daily living and communion is one of those important moment the faithful feel called to make this pious act of devotion.
The sign of the cross permeates a Catholic’s prayer life, from the public prayer of the Mass to private prayer around the dining room table. The priest opens Mass by leading the congregation in the Sign of the Cross. At the end of the Mass, he blesses the people “in the name of the Father, and of the Son, and of the Holy Spirit,” and they cross themselves as he blesses them. At home, when Catholics pray before meals, they usually open and close the prayer by making the sign of the cross. In Catholic schools, the prayers the school prays in common usually begin and end with the sign of the cross.
The sign of the cross often introduces and closes other prayers, but it is a prayer in itself and can also be prayed on its own. Sometimes Catholics make the sign of the cross, with or without words, at other times as well. Many Catholics will cross themselves when they pass by a Catholic church or chapel where the Eucharist is present. Some may make the sign as they drive past a cemetery as a quick prayer for the dead who are buried there. Sometimes Catholics may make a quick Sign of the Cross when receiving bad news, or when sirens pass, as a way of praying for those involved.
Praying the sign of the cross is so common that we often rush through it without thinking much about it. But the sign of the cross is an ancient tradition with deep theological meaning.
The sign of the cross, in words and in action, reminds us of the two central realities of our faith: who God is (the Trinity) and what God has done for us (the Cross). These are the core of why Catholics do the sign of the cross. - Why do Catholics make the Sign of the Cross?
We should constantly recall to ourselves when and if we make the sign of the cross at communion time that without the passion and death of Our Lord Jesus Christ on the Cross, we would have no Mass or Holy Communion.
Vatican City, Nov 22, 2017 / 03:40 am (CNA/EWTN News).- On Wednesday Pope Francis said that when we attend Mass, it is as if we are approaching Jesus on the Cross at Calvary, and that at every Eucharist we not only experience Christ’s redemption, but we participate in it.
“When we go to Mass, it is as if we go to Calvary, the same,” Pope Francis said Nov. 22. “This is the Mass: to enter into this Passion, death, Resurrection and Ascension of Jesus.”
Piety has its own good manners.1
To that end, the Church establishes norms for the proper gestures and postures of the Congregation at Mass.
Even though it says in the section Reception of Communion:
Make the sign of the cross after you have received Communion. - Source: Gestures and Postures of the Congregation at Mass | adoremus.org.
I am yet to find a first hand Church document that says this.
Who would have thought one needed to go as far Down Under (Brisbane, Australia) to get an answer. This article Blessing Oneself When Receiving Communion says:
Crossing oneself after receiving Communion has never been an official Church teaching or ritual. Whoever taught the practice “a generation ago” was misguided. In the past many children were taught that they would be punished by God if they chewed the host, but that does not make it right! The priest does not bless himself when he takes Communion, so why should anyone else do so? The sign of the cross is reserved for blessing oneself with holy water on entering the church and at the beginning and end of Mass.
After receiving Communion, hands that have touched the Body of Christ and the chalice of his Blood should be clasped together reverently. As you say, the focus at this point of the Mass is on “receiving Jesus”, not on the Holy Trinity as such which is what the sign of the cross calls to mind.
The question then becomes what is the gesture of reverence when receiving the Eucharist and when is it made?
The answer is from General Instruction Of The Roman Missal, 160:
When receiving Holy Communion, the communicant bows his or her head before the Sacrament as a gesture of reverence and receives the Body of the Lord from the minister. The consecrated host may be received either on the tongue or in the hand, at the discretion of each communicant. When Holy Communion is received under both kinds, the sign of reverence is also made before receiving the Precious Blood.
- Questions & Answers on Changes in the Mass, Gestures and Postures I |adoremus.org.
- Library: Gestures of Worship: Relearning Our Ritual Language - Catholic Culture. Note: no crossing oneself here after Holy Communion.
1. 541 Piety has its own good manners. Learn them. It's a shame to see those 'pious' people who don't know how to attend Mass — even though they go daily, — nor how to bless themselves (they throw their hands about in the weirdest fashion), nor how to bend the knee before the Tabernacle (their ridiculous genuflections seem a mockery), nor how to bow their heads reverently before a picture of our Lady. - The Way > Holy Mass > Number 541 | St. Josemaría Escrivá.
The simple answer is, it is "optional". The faithful has freedom from doing it as long as he/she do it reverently as Church Teaches. Bottomline, if it is "optional" it will always do us good if we do it as a way of forming good habits of making the "sign of the cross" as a way of acknowledging the presence of God in our minds especially in our hearts. Also, it is a sign of humility as the Cross is a sign of the Great Sacrifice of God to show His Love and Mercy for all of us. It is therefore a very good and pious to develop such a habit.
for a detailed ANSWER let's further explore some references;
The sign of the cross (Latin: signum crucis), or blessing oneself or crossing oneself, is a ritual blessing made by members of most branches of Christianity.
The sign of the cross is a prayer, a blessing, and a sacramental. As a sacramental, it prepares an individual to receive grace and disposes one to cooperate with it. The Christian begins his day, his prayers, and his activities with the Sign of the Cross: "In the name of the Father and of the Son and of the Holy Spirit. Amen." In this way, a person dedicates the day to God and calls on him for strength in temptations and difficulties. John Vianney said a genuinely made Sign of the Cross "makes all hell tremble."
Roman Catholicism draws a distinction between liturgical and non-liturgical use of the sign of the cross.
The **sign of the cross is required at certain points of the Mass:**
the laity sign themselves during the introductory greeting of the service,
before the Gospel reading (small signs on forehead, lips, and heart),
and at the final blessing;
other times during the Mass when the laity often cross themselves are during a blessing with holy water,
when concluding the penitential rite,
immediately after receiving Communion,
and when concluding private prayer after Communion.
In the ordinary form of the Roman Rite the priest signs bread and wine once before the consecration. In the Tridentine Mass the priest signs the bread and wine 25 times during the Canon of the Mass, ten times before and fifteen times after they have been consecrated. The priest also uses the sign of the cross when blessing a deacon before the deacon reads the Gospel, when sending an Extraordinary Minister of Holy Communion to take the Eucharist to the sick (after Communion, but before the end of the Mass), and when blessing the congregation at the conclusion of the Mass.
So to answer why do Catholics makes the Sign of the Cross in the Eucharist?
The short answer is, it is “optional”.
Since it is under optional, it will now be subject to individual disposition. God has given every souls a “freewill” to act with freedom in the manner of choosing what they think is right and beneficial to their soul.
Your next specific question;
“I know that no where in the Catholic Rite of Communion does it state that the communicant must make the sign of the cross after reception of the Eucharist in either species. So why is it that so many children are taught to do so in preparation of their First Eucharist?”
Why is the Children taught to do so?
The prudent question to ask next is, since it is optional. Will it bring good to the children to practice making the sign of the cross after receiving the Eucharist?
The answer is YES!, if we based it in the meaning and benefits of making the sign of the cross and its SIGNIFICANCE.
Below is an interview by ZENIT with the author Bert Gezzi on the “Significance of the Sign of the Cross.
The multifaceted significance of the sign of the cross has been investigated and explained by Bert Ghezzi, author of "Sign of the Cross: Recovering the Power of the Ancient Prayer" (Loyola Press).
Below is some of Ghezzi’s answers on the excerpt from the interview:
The sign of the cross is a very ancient practice and prayer. We don't have any indication of it in Scripture, but St. Basil in the fourth century said that we learned the sign from the time of the apostles and that it was administered in baptisms. Some scholars interpret St. Paul's saying that he bears the marks of Christ on his body, in Galatians 6:17, as his referring to the sign of the cross.
Tertullian said that Christians at all times should mark their foreheads with the sign of the cross. I can imagine that Christians would make a little sign of the cross with their thumb and forefinger on their foreheads, to remind themselves that they were living a life for Christ.
The sign means a lot of things. In the book, I describe six meanings, with and without words. The sign of the cross is: a confession of faith; a renewal of baptism; a mark of discipleship; an acceptance of suffering; a defense against the devil; and a victory over self-indulgence.
When you make the sign, you are professing a mini version of the creed — you are professing your belief in the Father, and in the Son and in the Holy Spirit. When you say the words and pray in someone's name you are declaring their presence and coming into their presence — that's how a name is used in Scripture.
The sign of the cross is a mark of discipleship. Jesus says in Luke 9:23, "If any man will come after me, let him deny himself, and take up his cross daily, and follow me." The word that the Fathers of the Church used for the sign of the cross is a Greek word that is the same as what a slave owner put on a slave, a shepherd put on a sheep and a general put on a soldier — it's a declaration that I belong to Christ.
When suffering comes, the sign of the cross is a sign of acceptance. It's remembering that Jesus became a man and suffered for us and that we participate in Christ's suffering. The sign of the cross says, "I am willing to embrace suffering to share in Christ's suffering."
One of the main teachings of the early Church Fathers is that the sign of the cross is a declaration of defense against the devil. When you sign yourself, you are declaring to the devil, "Hands off. I belong to Christ; he is my protection." It's both an offensive and defensive tool.
For full interview link: https://www.ewtn.com/library/liturgy/zsigncro.htm
Now, I only mentioned Seven significance of making the Sign of the Cross and there’s a lot more articles and saying coming from the Church Fathers & Saints.
St. Montfort book Love of Eternal Wisdom said that “Wisdom is the Cross”, so by teaching children to practice making the sign of the cross even on matters of optional requirement it is a sure path of obtaining graces to acquire Wisdom.
As an elder or those Catechist teaching the child, they are teaching the children for the good of their souls.
In closing, the Why’s of making of the Sign of the Cross after receiving the Holy Eucharist and teaching this practice as early to the children although “optional” is a pious act that will bring benefits in the growth of holiness in every child.