"Upon you my fellow servants, in the name of Messiah I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins; and this shall never be taken again from the earth, until the sons of Levi do offer again an offering unto the Lord in righteousness." (D&C 13)
There are three priesthoods: Aaronic, Melchizedek and Patriarchal. To be rightly called a priesthood, they must include associations with the powers of heaven.
This priesthood was given for condemnation; to seal up the children of men to the hardness of their hearts, or to lift them. When the children of Israel refused to come into the presence of God they were cursed with this lesser priesthood. This priesthood includes the association of angels which include true messengers that have authorized messages. Isaiah, Ezekiel, Jacob, King Benjamin and Joseph Smith are examples of these. The office of the calling of angel is to call men to repentance, to declare the conditions of repentance such that they may enjoy a greater priesthood if they are true and faithful.
Melchizedek (The Holy Order after the Order of the Son of God)
This priesthood is an association with the Savior or Second Comforter. It is not obtained by father or mother or by the will of men, but comes directly from God himself who employeth no servant there. The purpose of this priesthood is to help those who are true and faithful to enjoy a greater priesthood.
This priesthood brings us into association with the Great Patriarch, God the Father. We see an example of this priesthood when Nephi is having a dialogue with both the Father and the Son.
Joseph sought for the saints to obtain these last two priesthoods, which they had previously forfeited. The Lord set the conditions, and Joseph delivered the conditions of repentance to the saints. Those conditions were never fulfilled. (D&C 124)
These associations, or priesthoods are not limited to men, and indeed cannot be obtained by men without a woman.
We can continue to assert that the Nauvoo saints were faithful and that we have a fulness now, but by doing so we damn ourselves because we do not seek for what we could obtain, by the means appointed to obtain them.