"There is no limit to the height to which a woman may aspire in service to Christ" - John Alley
This question can be a difficult question for people, and is certainly an emotive one. But there is a positive answer that will satisfy most people, as it does the many men and women we know and are in relationship with. This question has been much more comprehensively addressed in the book, "The Apostolic Revelation" by John Kingsley Alley. Any serious consideration of this question should include a thorough reading of Chapter 6 of this book.
The Position of Women in the Old Testament
In the Old Testament, as a rule, all anointing for ministry was for men. Men had all the leadership, all the authority and all of the anointings. Men were placed in all of the offices — all the kings were men (i.e. there was no anointed queen), all the priests were men, and generally all the prophets. In the main, God’s dealings as far as appointing leaders is concerned, were exclusively with men, and leadership was always supposed to be upon men, unless God made an exception. And there were exceptions! Notably Deborah the Judge, and Miriam the Prophetess (Moses' Sister).
So in the Old Testament the established pattern was that all anointed leaders were men unless God made an exception.
But at the end of the Old Testament however we find a prophecy with a promise of bigger things to come. "And afterward, I will pour out my Spirit on all people. Your sons and daughters will prophesy, your old men will dream dreams, your young men will see visions. Even on my servants, both men and women, I will pour out my Spirit in those days." (Joel 2: 28-29). This promise showed that a new day was coming.
Women in the New Testament
In the New Testament, all anointings are for men and women equally, unless again, God makes an exception. Everything in the church is for both men and women, unless God makes an exception — and it so happens that there are some apparent exceptions. But of those exceptions, which we will discuss in a moment, God can and does also make exceptions. Just as the Lord made exceptions to His general method in the Old Testament, He is as free and well able to make exceptions to the usual governmental rule of the New Testament.
The exceptions made apparent in the New Testament appear to be two - eldership and apostleship. These two points are discussed in further detail in the book.
Thus in summary, in the New Testament generally all anointings and giftings are available equally to women, but with the usual exception being the eldership and apostleship. At the same time, we must allow for grace, calling and the work of the Holy Spirit to make exceptions to this general rule as He wills.
Exceptions to the Exception
Therefore, in the same way that God made exceptions in the Old Testament so as to bring certain women to positions of significant leadership, God can also make exceptions to his New Testament exceptions.
We need to be thoughtful in realising that Miriam and Deborah are not in roles equating to apostles and elders. In the New Testament we have not one clear example of a women in either of those positions. These are the two positions of not only significant gate keeping for the Body of Christ against deception, and high level demonic powers, but these are the most authoritative governmental positions in the Body of Christ at large. For Eldership, in practice the Scriptures say 'husband of one wife,' which seems to be significant.
There are many great female leaders, some leaders of local ministries, and some of big international works. We greatly honour them and recognise the grace given to them. Women who serve the Lord are worthy of our respect and we consider them to be a gift from God to the Body of Christ.