I was recently asked this question and so I thought I might take a moment to share my feelings on the subject. First of all, mormon.org has a statement by President Gordon B. Hinckley (prior President of The Church of Jesus Christ of Latter-day Saints) on the subject. He said,
“Women do not hold the priesthood because the Lord has put it that way. It is part of His program. Women have a very prominent place in this Church. Men hold the priesthood offices of the Church. But women have a tremendous place in this Church. They have their own organization. It was started in 1842 by the Prophet Joseph Smith, called the Relief Society, because its initial purpose was to administer help to those in need. It has grown to be, I think, the largest women’s organization in the world... They have their own offices, their own presidency, their own board. That reaches down to the smallest unit of the Church everywhere in the world...
“The men hold the priesthood, yes. But my wife is my companion. In this Church the man neither walks ahead of his wife nor behind his wife but at her side. They are co-equals in this life in a great enterprise.”
I believe that women do not hold the priesthood because that is God's plan. Having said that, I know with all my heart that God loves his sons and daughters equally. We, His sons and daughters, have different roles or responsibilities to fulfill in His plan, and by working together in our different roles, we are each happy, fulfilled and able to bless the lives of His children upon this earth.