I wrote an article on headcovering in the Antiochian Church, once you read it you will find the reason your priest did not openly say yes or no, basically it is because the Antiochian bishops have left it to the discretion of the woman:
The Tradition of Women Covering their Head when They Pray
For nearly two thousand years, Orthodox women, according to the words of the holy Apostle Paul, have gone to God's church with covered heads. Until recently, this custom has been kept by faithful women and has been handed down from generation to generation. It is a custom not only of the local churches, but also in world-wide Orthodox churches, whether one is in the Greek, Antiochian, Russian, eastern European, or African Orthodox Church, women in the church have their heads covered.
In the United States since the 1960s ( after the Roman Catholic decision of Vatican II that women did not have to cover their heads), some Orthodox women have chosen not to follow this custom. They have felt that it was dated custom that had no place in the practice of modern Orthopraxis. While head coverings are still the norm in the "old World", the response to this is varied by the jurisdictions in the United States. In most Russian and Slavic Churches, head coverings are still required and a woman is not communed without a head covering. In the Greek, Antiochian, and many OCA parishes head coverings are not required and the practice is left as a pious custom that women may use or not use as they wish. Many parishes, like ours, have head coverings for women who wish them but do not require them.
SCRIPTURAL BASIS FOR WOMEN COVERING THEIR HEADS
We find the basis for this pious custom of covering the head in Sacred Scripture itself, in the New Testament. The Most Holy Virgin Mary covered her head in the holy temple from her young years. According to tradition, her veil (head covering) in the Jerusalem temple was light blue; therefore, on the feast days of the Theotokos, Orthodox clergy often wear light blue vestments. The Most Holy Theotokos wore a veil (head covering) as a sign of her humility and submissiveness to God's will, which was manifested on the day of the Annunciation. Later the Apostle Paul reiterated the importance of this when he addressed the model for men and women as they prayed:
"Be ye followers of me, as I also am of Christ. Now I praise you, brethren, that in all things you are mindful of me and keep my ordinances as I have delivered them to you. But I would have you know that the head of every man is Christ: and the head of the woman is the man: and the head of Christ is God. Every man praying or prophesying with his head covered disgraceth his head. But every woman praying or prophesying with her head not covered disgraceth her head: for it is all one as if she were shaven. For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head. The man indeed ought not to cover his head: because he is the image and glory of God. But the woman is the glory of the man. For the man is not of the woman: but the woman of the man [c.f. Genesis 2-3]. For the man was not created for the woman: but the woman for the man. Therefore ought the woman to have a power over her head, because of the angels. But yet neither is the man without the woman, nor the woman without the man, in the Lord. For as the woman is of the man, so also is the man by the woman: but all things of God. You yourselves judge. Doth it become a woman to pray unto God uncovered? Doth not even nature itself teach you that a man indeed, if he nourish his hair, it is a shame unto him? But if a woman nourish her hair, it is a glory to her; for her hair is given to her for a covering. But if any man seem to be contentious, we have no such custom, nor the Church of God [i.e., if anyone want to complain about this, we have no other way of doing things, this is our practice; all the churches believe the same way]. Now this I ordain: not praising you, that you come together, not for the better, but for the worse. " (1 Corinthians 11:1-17)
According to St. Paul, Orthodox Women veil themselves as a sign that His glory, not theirs, should be the focus at worship, and as a sign of our submission to authority. It is an outward sign of our recognizing headship, both of God and man, and a sign of our respecting the presence of the Heavenly Hosts at the Divine Liturgy. In veiling, we reflect the divine invisible order and make it visible. This St. Paul presents clearly as a practice of all the churches of his time.
THE ARGUMENT AGAINST HEADCOVERINGS
Faithful Orthodox women who choose to not cover their head in church note that they believe that St. Paul was speaking as a man of his time, and that this ordinance no longer applies in modern context. They view this often more as a custom from the old world and not one that translates well into modern life. An example given is that in the "Old Country", Orthodox married women always had a head covering on to identify themselves as married and to help them protect themselves from the elements (much like to bonnets of pioneer women in the early US history). Women who choose not to wear a head covering note that several jurisdictions in the United States no longer require this custom after 1960s choosing to leave it a practice of personal piety. As a result of these issues they see no mandate for the continued veiling of American Orthodox women.
Often the detractors of those women who choose not to veil will judge them by saying their only reason for not veiling is that "veils and headscarves are not in style" or "I don't want to spoil my hair style". The reality is that for the faithful Orthodox Woman, who chooses not cover her head, there is no spiritual value to their covering their heads and so they choose to not cover their heads.
THE ARGUMENT FOR HEADCOVERINGS
Faithful Orthodox women who choose to wear a head covering (veil) believe that in doing so she recalls the image of her who was vouchsafed to carry the Savior Himself. If the Most Pure and Most Blessed One herself had a covered head, shall we really consider the imitation of her as foolish or old fashioned? To these women every outward action, accompanied by the correct Christian inward disposition, brings benefit to the soul. The action of wearing a head covering is one of obedience to the Holy Scripture and the tradition of the Church. The act is so rich with symbolism to these women. They often note that it is a "submission to authority", "a surrender to God", "an imitation of the Most Holy Theotokos as a woman who uttered her "fiat!"; "the covering of my glory for His glory", and a sign of modesty and chastity. Many converts feel that the veil is a symbol of their adoption into the Holy Orthodox Church through all of the ages and the women who are their spiritual ancestors and examples. One person interviewed noted that in all the icons of Holy women, the one common point of most is the covering of their head by veil or scarf.
Just as there are detractors for those who choose not veil, those who choose to cover the head in church have their detractors who will judge them as "old fashioned and out of touch with the modern church", or " too legalistic". The reality is that for the Orthodox Woman, who chooses to cover her head, there is real spiritual value and identification with the Church in the covering of their head and so they cover their heads.
TO VEIL OR NOT TO VEIL?
The Antiochian Archdiocese does not require women to cover their heads in church. Our bishops have wisely determined that this act is a voluntary pious act that has meaning to one who does it and understands why they do it. They do not require it, as an act of obedience, for those to whom it has no spiritual value. The greatest danger to our spiritual life is not whether a woman chooses to veil or not veil herself when praying, but lies in our judging her decision to do so, for when we so judge we put our own salvation in peril.