Hi, Henry —
We've answered this before. It's in the data base.
Briefly the New Testament Priesthood has nothing to do with Levitical priesthood instituted under the Jewish law. Our Priesthood is according to order of Melchizedek; check out the book of Hebrews. Melchizedek came along in Genesis 14, long before the Levites. As the author of Hebrews says:
Abraham tithed to Melchizedek, while Levi was still in his loins. (Hebrews 7:10)
Actually, Levi was a son of Jacob, who was a son of Isaac, the son of Abraham. Our ministerial priesthood participates in a unique way, and is indeed the priesthood of Jesus Christ in Personae Cristi Capo.
Our baptismal priesthood (or as the Protestants call it, the Priesthood of believers) is likewise a participation in the same priesthood of Christ, but not in the same way.
The word Priest is a latinized version of Prest which is a Greek abbreviation for Presbyter.
Now to the point about the Last Supper. This is an argument from silence, that has no other tradition to back it up, whether it be upper or lower case "T" on the tradition. There is no case in Church history where we see Holy Orders being conveyed to women.
Christ was a man and His Body the Church is the Bride of Christ. The priest stands at the altar in the stead of Christ, the man, and makes Him present first through the Sacrament of Holy Orders so that when the Priest speaks the words of institution, it is Christ, the man, speaking through the priest, the man. And of course, then Christ becomes present under the appearance of bread and wine in the Eucharist. So the priest takes on the role as groom. A woman can't be a groom — Period — end of story — exclamation point!
Again regarding the presence of woman at the Last Supper, there is no such Jewish law. Families would gather together to celebrate the Passover so, Yes, woman would be present at the Passover meal, but even if they were, it doesn't mean Christ ordained them for the New Covenant.
The texts in which we see ordination is in John's Gospel. And I hate to break it to you but according to John's Gospel it was not the Passover meal. According to John, the Passover was going to start so the bodies were removed from the crosses early and the bones of the two thieves were broken and we know the rest of the text. So John doesn't harmonize historically or chronologically with the synoptic Gospels.
And we read further in John's Gospels after the Resurrection, the Lord breaths on the twelve and says, "Receive the Holy Spirit, whoever sins you forgive will be forgiven...." (John 20:22-23) This is different from Luke's Pentecost account. So we see special authority given to these men, that is not given to all believers when the Spirit is poured out on all flesh in Acts Chapter 2.
May God richly bless you all.