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.
Nevertheless, despite my skepticism I have to ask, "Is this the will of God anyway?" It could be: "My thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts" (Is. 55:8-9). In the presence of God it may turn out that giving the priesthood only to men makes perfect sense, though it does not make sense in the terms of the world we inhabit.
To non-believers that looks very much like a cop-out, one made especially easy by the fact that I am male. To some Mormons it may also look like one. It is possible that it will turn out to be one.
But if I believe in God, then his greater understanding is always a genuine, possible explanation of what perplexes me. I can try to understand him and his work. I should try to do so. I can ask questions about it and ask for explanations. Since he is omniscient, however, I have to believe that he understands things that I do not. Thus, although I cannot explain the Mormon exclusion of women from the priesthood, because I trust in the Restoration as a whole my working assumption is that what seems to be a problem is part of some divine plan or work that I do not yet understand.
Suppose, however, that it is not. Suppose that giving only men the priesthood is a consequence of the "foolish traditions of our fathers" (Alma 30:14), as I believe the exclusion of Blacks from the priesthood was, rather than a divine prohibition. Even if so, I assume that God has a reason for not yet correcting that false tradition through his prophet.
Mormon revelation says that God speaks to us in our language and weakness (D&C 1:24). When he speaks, he takes our cultural and historical situatedness into account. Perhaps we are not yet ready for such a change: not yet ready to hear it, not yet ready to live it . . . I don't know. But my trust in the witness of the Spirit supports me in the face of my rational difficulties.
That's the nature of trust, of faith. In ordinary life to trust someone is to rely on that person's integrity in the face of circumstances or events in which one might otherwise be skeptical. It is to have confidence in the judgment of another even when that judgment can't be independently verified.
I trust Janice because, having been married to her for forty-one years, I know she is a person of integrity, a person I can trust. She is faithful. As a result, even when faced with what might otherwise seem perplexing behavior, I am not concerned. It isn't that I am concerned about something and then overcome that concern by recalling her integrity and faithfulness. Rather, I trust her, period. I am not concerned to begin with.