Of Both Kinds
The Cup of the Lord is not to be denied to the Lay-people: for both the parts of the Lord's Sacrament, by Christ's ordinance and commandment, ought to be ministered to all Christian men alike.De Utraque Specie
Calix Domini laicis non est denegandus, utraque enim pars Dominici sacramenti, ex Christi institutione et praecepto, omnibus Christianis ex aequo administrari debet.
Archbishop Peter Robinson
Article 30 is one of the simplest of the Articles of Religion. The Cup had gradually been withdrawn from the laity for pragmatic reasons during the Dark Ages. The usual reasoning being to prevent the "irreverence" arising from long mustaches dangling in the chalice. Whilst this may have been a legitimate concern, it still went against what Jesus instructed His disciples to do, which is to eat and drink in amnesis of Him.
The issue of the Cup had been raised a little over a hundred and twenty-five years previously by the Hussites or Bohemian Brethren, who demanded the restoration of the Cup to the laity and practiced it in their own congregations. It was among the concessions the Papacy was prepared to make in order to end the Hussite schism, but it was to be another 500 years before they would grant permission for the laity throughout the Latin Rite to 'drink of that Cup' as our Lord commanded. Even then, the Vatican II Council gives only conditional permission for the laity to receive the Cup.
The other element stresses the priesthood of all believers in that it says that the Cup ought to be administered 'to all Christian men alike.' Anglicanism shares with Lutheranism a very strong sense of both the priesthood of all believers, and also of the need for a ministry of Word and Sacrament set apart by prayer and the laying on of hands. Both are strictly Scriptural. Unlike the Roman Church we do not believe that ordination makes an ontological change in a person, but rather sets apart a man to certain functions - the administration of the sacraments and the preaching of the Word.
Fr. Robert Hart
In English speaking countries the Roman Catholic Church uses modern language translations of the Mass. They come to the words of the Lord about the cup, "Drink this all of you." The use of the vernacular instead of Latin may be one of the reasons that they began offering the chalice to laity.
But, in some places they still refuse the chalice to laity, as if ignoring the very words of Jesus. The doctrine of concomitance is the rationale. That Roman Catholic doctrine teaches that the whole Christ is present under each separate Eucharistic species. Therefore, they teach, the Body and Blood, Soul and Divinity of Christ are present fully in each of the consecrated elements. Many Anglicans have accepted this same doctrine, but they apply it in practice only to the reserve sacrament that they carry out of the church to those who are sick or otherwise unable to come.
It is not my purpose here to argue either for or against concomitance. I will say only that it is not based on any revelation taught in Scripture, so I cannot simply affirm it as dogma. The issue here is one of the Church obeying her Lord. Reading the words of Jesus as translated into plain English, and then refusing the chalice to the laity, is a clear example of why it is difficult, indeed, to ascribe much good to Newman's Theory of Doctrinal Development. Based on a scholastic bit of reasoning, developed by human reason to the status of revealed dogma, the word of the Lord is set aside. I am not disputing the doctrine, but merely pointing out that it is used as a rationale for open disobedience to the very words of Christ, something no one has the authority to do.
In our Prayer Book Holy Communion we use older English: "Drink ye all of this." The problem with that is the way it sounds to modern ears. As a child I thought it meant to drink it all, and waste none of it. I did not understand that "ye all" meant "all of you" - like the quaint Southern expression, "y'all." When I celebrate I try to make the actual meaning come across to modern ears, even Northern ears, which requires seeing two commas where they really were not placed. Thus, when I am at the altar it comes out, "Drink, ye all, of this." I have had people comment that they finally got it.
Aside from simply obeying the Lord, some have speculated that each element, once consecrated, imparts a specific grace. This idea was at least mentioned by E.J. Bicknell in his excellent book about the Thirty-Nine Articles. Our Prayer of Humble Access contains words that can reflect an old idea that the Body of Christ cleanses our sinful bodies, and His blood washes clean our souls, as separate actions. The actual words in the Prayer are fine when interpreted along different lines, such as remembering that by the Risen Body of Christ, our own bodies will rise free from the uncleanness of death, etc. Nonetheless, the idea of separate operations of grace is purely speculative at best. It cannot be proved by Scripture, and has not been taught by most of the Church.
Personally, I prefer the idea of concomitance over that idea, or rather, I prefer something to the effect that the communicant receives the fullness of God's grace through faith while receiving the sacrament. I have had a young man kneel at my altar rail, willing only to drink from the chalice, but not to eat. For medical reasons, he must not consume wheat. I cannot imagine God withholding any grace from him on that basis. In addition, it is clear that a preoccupation with trying to understand how God through the sacrament imparts grace (which is not understandable with the mere human mind) distracts us, all too often, from remembering the Lord's sacrifice as we partake of His covenant supper together as the Church.
In the final analysis, however, to withhold the chalice from the laity, when present at the actual celebration of the Eucharist, is simple disobedience to Christ Himself. It flatly contradicts His clear instruction. And, as I said, that is something no one has the authority to do.