There were plenty of women preachers, however. I've preached at worship services in Orthodox churches, myself.
We have some semantic confusion here, because many things Protestants consider restricted to clergy are done by Orthodox laity. We have women saints who were missionary evangelists, church-planters, teachers, healers, preachers, apologists, spiritual mothers, counselors, miracle-workers, martyrs, iconographers, hymnographers, and theologians. Holy women do virtually everything men do, except stand at the altar. That leaves the rest of the world—which is where most of God's work gets done.
St. Theodora the Empress exercised authority over both men and women, and brought a triumphant end to the destruction of icons. St. Nina, a 14-year-old slave, evangelized the entire nation of Georgia. St. Mary Magdalene, St. Helen, and others are called "Equal to the Apostles." St. Catherine and St. Perpetua were brilliant debaters.
So I don't mind if Protestant denominations want to ordain women. Many times, this just means allowing them to do things Orthodox women have always done.
Even if we know the Orthodox Church's stance on the question of women priests, we still don't know how they got there. Strangely enough, in the vast writings of the early church the question of women's ordination never comes up. It seems it just was never controversial. Throughout the ages, Orthodox women and men found the all-male priesthood a satisfactory, maybe even a positive, thing. How can we see what they saw?
What Saint Paul Said About Women in the Church
I don’t think we'll get much help from the usual arguments. Opponents of women's ordination often start by citing St. Paul's requirement that women be submissive and silent in church (1 Timothy 2:11-15 and 1 Corinthians 14:34-35). Yet this can't mean utter silence, because Paul honors many women in active ministry, like the deaconess Phoebe (Romans 16:1). And he hails Euodia, Synteche (1 Corinthians 4:2-3) and Prisca (Romans 16:3) as synergoi (fellow-workers) in the gospel. Vocal prophetesses are found everywhere in the Bible, from Moses' sister Miriam (Exodus 15:20) to the four daughters of St. Philip (Acts 21:9). The prophetess Anna spoke out in the temple, telling everyone about the child Christ (Luke 2:36-38).
When read in context, it sounds as if St. Paul is concerned about disorder in worship. In 1 Timothy, he admonishes men to pray "without anger or quarrelling" and tells women to be "in hesychia," a state of prayerful stillness. In 1 Corinthians, Paul says it is "disgraceful" when women talk in church, and equally "disgraceful" when they pray without wearing a veil. Yet few who stand on the former text make a similar insistence on women wearing veils.
Here's another common argument: a priest must be male because he represents Christ. When I was attending a mainline seminary and aiming toward ordination myself, I would say, sure, Christ was male, and he was also Jewish, and a certain height and hair color. Why isolate only his maleness as indispensable? Surely the fact that he was Jewish is even more significant, but we don't exclude from ordination people who don't have Jewish blood.
We don't find this argument used in the early church; in fact, early Christians reflected very little on why Christ was male. All their attention was focused on the fact that he was human. As Bishop Kallistos Ware points out, Christ's maleness isn't even mentioned in the hymns appointed for the Feast of the Circumcision, which would seem the likeliest opportunity. There might be good practical and theological reasons why Jesus was born male, but the early church did not explore them.
Another familiar line goes, "But we’re not putting women down. Women and men are equal. They just have different roles." Okay, but this still doesn't answer the question. Sure, every person has a unique calling, and every role is "different" from every other. What is it about the priesthood that requires maleness?
In 1988 an Orthodox consultation met in Rhodes and considered some aspects of women's ministries. They recommended resuming the lapsed practice of ordaining women deacons, and they suggested that in the all-male priesthood there was a correspondence between the priest and Christ, and between the Virgin Mary Theotokos and the Church.