Inspired by an Ancient Faith Radio interview with Metropolitan Kallistos Ware, here are some developing thoughts for why the priesthood is male rather than of both male and female.
Firstly, the priesthood is not exclusively for males. All Christians are members of the royal priesthood offering spiritual sacrifices to God. This is particularly in the case of offering their own bodies. Being a priest seems to be part of being a created person or hypostasis of which also angels share to a degree. If this is the case why are there not women ordained to the presbytery because they are indeed priests? The answer to this question comes from an important distinction found in the Fathers, particularly St John Chrysostom. This distinction is between public and private roles. Thus, there may be different rules for what can happen in a public role and what happens in a private role. The presbytery as a public function of publicly ordained members serves as a public priesthood for the laity in communal worship. Each member of the laity privately serves as a priest in offering himself or herself to God as a living sacrifice.
Why though should the publicly ordained priesthood, the presbytery, be only male? The answer to this is found in an iconic manner. The difference between male and female is really only a matter of form, although there may be other differences these are only of a matter of degree and not fundamental differences, both share the same nature. Thus, the restriction of the public priesthood to men should be seen in the iconic sense that draws its symbolic strength from a distinction in form. Thus, in general, there is a readily identifiable distinction in form between male and female and this can be used to symbolically represent important theological truths or rather an incarnation of the divine in some aspect.
So what is the theological truth to be incarnate in a male priesthood, particularly the presbytery? This truth is that we only have one Teacher, Christ, and one Father in heaven. Yet each presbyter is a teacher and each one is called father. This would be a contradiction, and one that Protestants point out, unless one sees that a presbyter is the iconic presence of Christ, Himself, and the icon of the One Teacher and one Father in heaven. Thus, the presbyter is an icon of the Son of God, of God. The presbyter is a symbol of God for the laity, he stands in a relationship with the laity as God with man. He teaches as Christ, not as man, he is father as God and not as man. He does not perform a human function but a divine function. To establish this iconic relationship, the presbytery is restricted to males. This restriction is to establish that the presbyter is a divine task and not a human task. The distinction between male and female is the ideal ground of distinction to represent this. We see this throughout the Scripture particularly in the case of marriage where this iconic representation is clearly laid out, particularly by St Paul. The most important teaching of St Paul though that establishes this iconic role is when he speaks of men being the image and glory of God and women the glory of men. St John Chrysostom says that the image of God is primarily found in the governance of man particularly over the rest of creation and this is particularly seen in the role of the presbytery, who are appointed to govern the Church. (This is also why women should not have authority over nor teach men in a public context because this would symbolise man teaching or having authority over God. Although in a private context there is some room for this to reflect that we all are created in the image of God, male and female and are all members of the royal priesthood. This iconic function is also why women should cover their heads to symbolise the obedience that man is to show to God, particularly after the Fall which was caused by disobedience. To not wear a covering is symbolically to deny the need of man to be under obedience to God and thus to remain in the original disobedience of the Fall and would be a failure to teach by action how each human person must approach God.)
Thus, the restriction of the public priesthood to male only is an important iconic symbolisation to establish the proper relationship between God and man. The presbytery is not about men leading men but about God leading men and as such the restriction to males only is essential to maintain this mystery. Ordaining women to the priesthood would be to symbolically reduce the presbytery to a human function of men leading men expressing the opinions and teaching of men and there would be no counter to the Protestant claim that the Church is not scriptural by having teachers other than Christ.