Something Else I Don't Know
Their desire to have such positions might appear to be a desire for authority over others and, therefore, to some degree something unrighteous. But more often the desire seems to manifest a concern that women are more-or-less hidden from church leaders by their exclusion from priesthood positions. Presumably having women in positions of priesthood leadership would make them more visible in the Church as a whole.
Those with this concern have difficulty understanding how women can have a voice in the Church with little and sometimes no participation in its leadership. I assume that the relatively recent emphasis on governing with councils, which include women, is intended to help ameliorate that. But the highest of these councils, at the ward (congregational), stake (multi-congregational), and general church level, include no women.
Others who are concerned don't see the problem in terms of having priesthood authority. Some of the most powerful complaints I've heard are from those who don't understand why they would be only the recipients of God's power and never its vehicle. I have had memorable, powerful spiritual experiences that came through giving priesthood blessings. Those are experiences a Latter-day Saint woman cannot have except indirectly.
Of course an LDS woman is not left bereft of personal spiritual experience. In addition to the blessings that come through scripture study, prayer, and fasting, she can have the blessings of serving in the Church. She can be a leader of the women's, children's, or young women's organizations. These are all avenues through which an LDS woman can be blessed and can have profound spiritual experience. Yet in spite of that, some spiritual experiences are not directly available to her, namely those that come through exercising the priesthood.
Each of these kinds of difficulties goes beyond a complaint that women feel bad about not having the priesthood. Each comes down to a concern that, in spite of Mormon teachings, because the structure of the Church is patriarchal, women tend to be defined mostly in terms of their relation to men. They are not and cannot be prime actors.
Whether or not that is doctrinally necessary—and the temple sealing suggests that it is not—it is often culturally true. Mormon men and women are as much part of contemporary culture as anyone else. Among other things, seeking to be perfected means seeking to find in Christ's gospel lives that go beyond the negative effects of that culture. The question is, "Is this Mormon teaching and practice divinely revealed or is it merely the consequence of our history?"
I can't explain the LDS Church's exclusion of women from the priesthood. I cannot tell you why it is so. I'm skeptical that any mortal can, though I could be wrong. I'm not the prophet. Nor am I a historian of Mormonism, nor any more than an amateur scholar of Mormon beliefs. My skepticism isn't based on my authority, church or scholarly. Instead it stems from the fact that most of the explanations I've heard seem post hoc.
James Faulconer is a Richard L. Evans Professor of Religious Understanding at Brigham Young University, where he has taught philosophy since 1975.