In the biblical verse you quoted, it states, "Do not stop him." It did not say "her." God will not go against His own will. From the beginning, He gave man to be the role to be priests. Even in the Old Testament, God's chosen people (the Jews) did not have female priests. God called only men to be priests because men are the head of the household. Members of the Church are God's family. And in the family, the man is the Head of the household. Women are not called to be the head of the household. And because they are not the head of the household, they are not supposed to be priests because priests represent Christ, who is Head of the Church. In the Old Testament, all the prophets that God chose were men. All His annointed ones were men.
All of Heaven recognize the man to be the head of the house. Even the angel went to Zachariah to tell him that his wife Elizabeth was going to have a child. The angel did not go to Elizabeth to tell her this because she was not the head of the household. He went to Zachariah. In the case of Mary, the Angel Gabriel went to Mary to tell her that she will give birth to the Son of the Most High. At that time, Mary was not yet married. However, AFTER Mary and Joseph were married, the Angel appeared ONLY to Joseph because Joseph was the head of the household. The Angel no longer appeared to Mary after she married Joseph. It was only to Joseph that the Angel spoke to. And this is an Angel sent by God.
Jesus also chose men to be His Apostles, and He instructed these men to go out and preach to the world and baptize them in the name of the Father, Son, and Holy Spirit. He did not tell any woman to do this. Therefore, the priesthood belongs only to the men because they represent Christ who is Head of the Church. The wife is not head of the household. The wife represents the Church and therefore cannot be a priest just as St. Paul says:
Ephesians 5:23 Because the husband is the head of the wife, as Christ is the head of the church. He is the saviour of his body.
The husband is the head because he represents Christ who is Head of the Church. The wife is the body because she represents the Church. This is God's plan in the role of men and women. The modern world disagrees with God's plan because the modern world thinks it knows better than God.