So many! How about this one, the doctrine the male priesthood. Obviously, as the former Pope stated, we cannot change this to suit society.
The ordination of women is an issue.
From NewAdvent.org /Woman, an excerpt of the Church's stance on it. Complete explaination at the site, the links are to various topics at the site itself.
.....priestess, deaconess, but they were so denominated because their husbands had been called to the ministry of the altar. There was, it is true, an order of deaconesses, but these women were never members of the sacred hierarchy nor considered such. St. Paul (1 Corinthians 14:34) declares: "Let women keep silence in the churches: for it is not permitted them to speak, but to be subject, as also the law saith. But if they would learn anything, let them ask their husbands at home. For it is a shame for a woman to speak in the church". The Apostle also says that in the church "ought the woman to have a covering over head, because of the angels" (1 Corinthians 11:10). It is not allowed to women, however learned and holy, to teach in monasteries (cap. Mulier, 20 de consec.). Ministering at the altar, even in a subordinate capacity, is likewise forbidden. A decree says: "It is prohibited to any woman to presume to approach the altar or minister to the priest" (cap. Inhibendum, 1 de cohab.); for if a woman should keep silence in church, much more should she abstain from the ministry of the altar, conclude the canonists.
III. Although women are not capable of receiving the power of sacred orders, yet they are capable of some power of jurisdiction. If a female, therefore, succeeds to some office or dignity..........
Catechism:
1577 "Only a baptized man (
vir) validly receives sacred ordination." The Lord Jesus chose men (
viri) 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 college of bishops, with whom the priests are united in the priesthood, makes the college of the twelve an ever-present and ever-active reality until Christ's return. 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.
1542 At the ordination of priests, the Church prays: Lord, holy Father, . . .
when you had appointed high priests to rule your people,
you chose other men next to them in rank and dignity
to be with them and to help them in their task. . . . you extended the spirit of Moses to seventy wise men. . . .
You shared among the sons of Aaron
the fullness of their father's power.
From: Catholic-forum.com, various lively discussions from links found in my search "ordination of women" that you may find interesting.
http://www.catholic-forum.com/forums/search.php?searchid=521466
AndyF