Cardinal Arinze speaks for himself in this YouTube video.
Fr Joseph Fessio makes a brief but systematic contribution to the debate here.
The Diocese of Lincoln, Nebraska, under the leadership of Bishop Bruskewitz, is the only diocese in the United States not to permit altar girls (which are only permitted with the express permission of the local bishop). There is an interesting short article on the subject on the diocesan website; in case it is taken down we reproduce it here.
'Seedlings', by Fr Christopher Kubat.
The question whether women can be admitted to the sacrament of Holy Orders continues to be raised, despite Pope John Paul II definitively saying in his apostolic letter entitled Ordinatio Sacerdotalis, “I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church’s faithful.”
Canon law states, “Only a baptized male validly receives sacred ordination” (can 1024). Further, the Catechism of the Catholic Church states, “Only a baptized man validly receives sacred ordination. The Lord Jesus chose men to form the college of the twelve apostles, and the apostles did the same when they chose collaborators to succeed them in their ministry … The Church recognizes herself to be bound by this choice made by the Lord himself. For this reason the ordination of women is not possible” (CCC 1577).
Are there any other reasons? Aren’t women smart, wise and hard-working enough, sharing the same dignity as men? Certainly. Some have argued that they are more sensitive and nurturing than men, something I wouldn’t disagree with. I would argue as a whole, women have a higher pain tolerance than men. How about natural courage? How many women and men were at the foot of the cross? These arguments, however, have nothing to do with the question at hand.
Once, while flying, I sat next to a woman who told me she was an Episcopalian priest. I asked her to define marriage. Thankfully she stated that marriage is for one man and one woman, because this constitutes another powerful argument. Yes, marriage is for one man and one woman (Gen 1:27; 2:24), something that Jesus the Eternal High Priest Himself re-iterated (Mt 19:4-6). In a beautiful vision, an angel said to John the evangelist, “Come, I will show you the Bride (referring to the Church, the mystical body of Christ), the wife of the lamb (referring to Christ Jesus the bridegroom)”(Rev 21:9).
St. Paul completes the connection in his letter to the Ephesians. In it, he exhorts wives to be subject to their husbands as the Church is to Christ, and husbands to love their wives as Christ loved the Church (this means that husbands are to mount the cross daily for their wives). Therefore, if the Catholic Church is the bride (feminine), and an ordained priest who stands in the person of Christ shares in this spousal relationship as the bridegroom Jesus Christ (male), it is necessary that candidates to Holy Orders be men. This is why the Church has no authority to admit women to the priesthood. It is about nuptials.
What about altar servers? On July 27, 2001 the Congregation for Divine Worship’s Letter on Altar Servers states that “no priest is obligated to have female servers, even in dioceses where this is permitted.” Why is this, since girls are as smart and capable as boys? Because many boys, myself included, first received their calling to the priesthood as altar boys, and when girls are allowed to serve, some boys fall away and lose interest.
Please pray for the young men who will be ordained to the diaconate May 28 and to the priesthood May 29. They are the ones who will forgive sins (Jn 20:23), offer the Holy Sacrifice of the Mass (Lk 22:19; 1 Cor 11:24) give us the Most Holy Eucharist, and anoint us on our deathbeds (Jas 5:14-15).