This is disallowed in the Coptic Orthodox Church, with solid scriptural backing. HG Bishop Youssef of the Southern United States diocese explains it in the following fashion:
Not only were many women noted in the ministry of Christ, but also as modeled by his Master, Jesus Christ, St. Paul's ministry also included the contributions of many significant women. Women have the right to teach and instruct, but not in the ecclesiastical role of the clergy or deacons, which include the services of the Divine Liturgies. Although St. Paul often exchanged identifying the husband and wife team of Priscilla and Aquila, or Aquila and Priscilla, a couple who often accompanied him in his travels and throughout his ministry, when they instructed the preacher Apollos on baptism and receiving the Holy Spirit, here, St. Paul mentions Aquila first, while at other times Priscilla would be mentioned first because of her extremely active role. "When Aquila and Priscilla heard him, they took him aside and explained to him the way of God more accurately" (Act 18:26). This deliberate notation is the correct protocol. Thus, they fulfilled their specific roles as laymen and women. Following this incident in the Holy Book of Acts 19:1-10, St. Paul administers the ecclesiastical rite through his bishopric apostleship by laying his hands upon those who having been baptized, had not yet received the Holy Spirit. Therefore, the message is clear, women may teach anyone who is need of learning about God. Spiritual nourishment is just as important as physical nourishment. When someone is hungry and thirsty for the knowledge of God, man, woman, and child are all called to respond and support them in their spiritual weaknesses and needs. However, when it comes to the ecclesiastical roles, these are exclusive to men, who are specifically appointed for these roles. Thus, Aquila did not have the authority of the priesthood to administer the Sacrament of Confirmation, but left this to the apostle Paul. The Holy Sacrament of the Priesthood was established by Christ Himself and enforced by all of His disciples and apostles. Inclusive in the Sacrament of the Priesthood are the ranks of deacons, who have other specific tasks and responsibilities. Therefore, women may teach in the classroom or even in a church building, but NOT during any ecclesiastical service or the Divine Liturgies, other than being members of the congregation.
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A great deal of respect is given to women in our Church, as is borne out even in the modern day with great figures like Tamav Irini, the recently departed (d. 2006) abbess of Abu Seifein convent in Old Cairo, whose biography and many sayings and miracles are famous and greatly cherished by the Coptic Orthodox people. And she is not alone in that respect, as the examples of the Desert Mothers and other saints like St. Demiana, St. Marina, etc. all show.
Everyone and everything in the Church has its proper place, and it's not for anyone to change how things are done for the sake of seeming progressive or modern when we are not a modern church to begin with. Others can have that, in accordance with whatever they follow. God has established His Church in Egypt as surely as anywhere, not men or women in post-Christian societies like in the West, with whatever desires they may have at any particular point in their move to or away from certain fashions of thought. The Church is above all that, thanks be to Christ our God Who is its chief cornerstone.
