Actually (and with much orthodoxy), we as Catholics do recognize that Mary was a priest. As a Jewish woman, the promise of God to the Israelites: “You shall be to me a kingdom of priests, a holy nation” (Ex. 19:6) would have been extended to her as well. This promise was to all the Israelites (Jews) and Mary was certainly one.
Mary was also the very first Christian. She was the first human being to accept Jesus. And St. Peter tells us: “You too are living stones, built as an edifice of spirit, into a holy priesthood, offering spiritual sacrifices acceptable to God through Jesus Christ” (1 Pet. 2:5). So, in a sense, she may very well be considered to be the first “priest” of the New Covenant who offered her own womb to God as a spiritual sacrifice through Jesus Christ.
God has made for himself a chosen race. . .a royal priesthood of believers which began with his promise to the Israelites in the desert and remains true today in the Christian community. We are all, in a sense, priests. We are all called to worship our Lord and God sacrificially through our lives in Jesus Christ.
SO, the Blessed Mother indeed WAS a priest, just as we are all. However, she was not an ordained priest of the Levitical priesthood (OT) nor was she an ordained priest of the New Covenant (NT). Neither of these ordained, ministerial priesthoods were open to women. These ordained ministries of the priesthood have never been appropriate functions of women.
I love our pastor’s explanation for why women can not be ordained priests. It includes such a wonderful understanding of the Blessed Mother. I’m paraphrasing here: Unlike the ordained priests in the Church, Mary is truly the only person in history who could actually look upon the body of Christ and say “this is my body, this is my blood.” And so, if any woman in the world could have said the words of concecration, it would have been her, yet even she was not called to the ordained priesthood.
We are all given roles in the priesthood of believers. Arguing about whether women should/could be priests is irrelevant, because we are! To demand “equality” in the ordained priesthood is to be ignorant of the beautiful and appropriate role God has prepared for women in this holy priesthood we have in the body of Christ, our great high priest!