Roman Catholic AnswerNo they are not, because under religious regulations of the Catholic Church teach it as such. In the New Testament priesthood is the priesthood of Christ Himself. All men who, through the Sacrament of holy Orders, have become priests (or bishops) participate in Christ's priesthood. And they participate in it in a very special way: They act in persona Christi Capitis, in the person of Christ, the Head of His Body, the Church. Christ, of course, was a man; but some who argue for the ordination of women insist that sex is irrelevant, and that a woman can act in the person of Christ as well as a man can. This is a misunderstanding of Catholic teaching on the differences between men and women, which the Church insists are irreducible; men and women, by their natures, are suited to different, yet complementary, roles and functions. We have to face the fact that the ordination of men is an unbroken tradition that goes back not only to the Apostles but to Christ Himself. As the Catechism of the Catholic Church (para. 1577) states: "Only a baptized man (vir) validly receives sacred ordination." The Lord Jesus chose men (viri) to form the college of the twelve apostles, and the apostles did the same when they chose collaborators to succeed them in their ministry. The college of bishops, with whom the priests are united in the priesthood, makes the college of the twelve an ever-present and ever-active reality until Christ's return. The Church recognizes herself to be bound by this choice made by the Lord himself. For this reason the ordination of women is not possible.
Still, the argument continues, some traditions are made to be broken. But again, that misunderstands the nature of the priesthood. Ordination does not simply give a man permission to perform the functions of a priest; it imparts to him an indelible (permanent) spiritual character that makes him a priest, and since Christ and His Apostles chose only men to be priests, only men can validly become priests. In other Words, it's not simply that the Catholic Church does not allow women to be ordained. If a validly ordained bishop were to perform the rite of the Sacrament of Holy Orders exactly, but the person supposedly being ordained were a woman rather than a man, the woman would no more be a priest at the end of the rite than she was before it began. The bishop's action in attempting the ordination of a woman would be both illicit (against the laws and regulations of the Church) and invalid (ineffective, and hence null and void).
The movement for women's ordination in the Catholic Church, therefore, will never get anywhere. Other Christian denominations, to justify ordaining women, have had to change their understanding of the nature of the priesthood from one which conveys an indelible spiritual character on the man who is ordained to one in which the priesthood is treated as a mere function. But to abandon the 2,000-year-old understanding of the nature of the priesthood would be a doctrinal change. The Catholic Church could not do so and remain the Catholic Church.
Another Answer from the rest of the Christian ChurchAs this question is posed in the 'Christianity' section, I find the above answer, which is only the opinion of some in the Roman Catholic Church as one-sided and does not represent the Christian Church as a whole.In many denominations - including the Anglican Church, women have an equal right to be bishops along with men. As for 'archbishops' - that is a different matter as an archbishop is simply a bishop that has been elected to be pastor to a group of dioceses known as a province, and is not an ordained position. So, if a woman has the right to become a biishop, then she would automaticallly have the right, if elected, to become an archbishop.
So, we must here concentrate on bishops per se as the bishop is the highest level of the ordained ministry, and also on the priesthood - as all bishops are alo priests.
This consectarion of women bishops in the Christian Churches that have bishops (apart from the RC Church) was not decided by the teaching of an organisation that has based its theology only partially on scripture, but mostly on the tradition of the Church teaching, some of which is fabricated and non-Biblical. Instead it was based on scripture and the practice of the early Church.
In the early Church women played as much of a role as men. In Paul's letters several women church leaders are mentioned - Priscilla and Lydia as examples. Taking Lydia, she was a prosperous businesswoman and dealer in purple cloth and head of her household. When she became a Christian, all her household were baptised and she became the church leader there. This would have meant presiding at the Eucharist as, even in the Early Church, we hear that the earliest Christians met to 'break bread as Our Lord requires'.
The origin of bishops was that of overseer. The Greek term for 'bishop' in the New Testament
Within the catacombs in Rome, frescoes of the early Church show women presiding at the Eucharist in a priestly role. The 'Fractio Panis' (google it!) is a fresco from a Christian catacomb showing clearly a Eucharist taking place - with the priestly celebrant very clearly anatomically female.
More that this, Paul also speaks of other women leaders such as Junia (Rom 16:7) whom, with her husband, he calls "eminent among the apostles". And there is a great deal of evidence that she too was an overseer in the early Church - and hence what we would now term a 'bishop'.
It wasn't until much later that the male of the species took over the running of the Church under the pretext that women have a 'special' role.... ('special', as long as it was subservient to the men).
There is an argument that the priesthood is 'Christ's priesthood' - in other Words, the priesthood went back to the sacrifical nature off the priest in the Temple. Catholics still believe in this sacrificial role of the priest as they believe in the mass as a resacrifice of Christ's body and call the table on which the Eucharist is placed an 'altar' as per the sacrificial altar in the Temple. However, when Christ came he removed that sacrificial necessity, dying on the Cross once and for all for everyone. So the sacrificial nature of the priesthood is removed for ever. The priest's role was not 'redefined' by Protestant Churches, as the priestly function of sacrifice has never been there since the Cross. Yet some Catholics fail to recognise this. In scripture we are told that all people who turn to Christ are completely clothed with Christ (see below) - not just men. And not just men who have been ordained.
So, in many denominations that base their theology on scripture and the early Church, women are allowed full rights to become priests and bishops. Many African Churches have women bishops as well as priests, as does the Episcopalian Church, Reformed Church and Methodist Church. The Church of England has had women priest since the 1990s and has just voted to appoint women bishops.
It is these forward-thinking churches that are carrying Paul's message on to the generations that follow us. As he wrote to the Galatian Church:
"So in Christ Jesus you are all children of God through faith, for all of you who were baptized into Christ have clothed yourselves with Christ. There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus. If you belong to Christ, then you are Abraham's seed, and heirs according to the promise." [Galatians 3:26-29]
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