Brigham teaches that Eve was allowed to partake of the fruit because one cannot be exalted without being subjected to the temptation of sin.
Brigham Young, "Providence—Ignorance of Sectarian Priests—Free Agency—Recreation, Etc.," December 27, 1857, Journal of Discourses, 26 vols. (Liverpool: Asa Calkin, 1859), 6:145
Before the Gospel revealed the introduction of sin to this planet, it was a great marvel even to the most learned, and they would ask, "Why was it so?—is it not strange?" and would rest with the expression, "It was suffered to be so." While reasoning or familiarly conversing with one another, let the question be asked, "Why was Eve suffered to partake of the forbidden fruit?" and the invariable reply was, "I cannot answer that question: it seems that it was so, and it appears to be a great pity." That is all the knowledge there is in the world on that point. The starting-point they have not learned, that no intelligent being could be exalted with the Gods without being subjected to the temptation of sin; that he might know and understand the power of the adversary, the opposite to goodness; for it is written that "There must needs be an opposition in all things." The world have not yet learned that simple truth.
I remember hearing a debate between brother Alfred Cordon, one of our Elders, and a sectarian priest, when I was in England; and I presume there were a score or two of priests ready to put questions and answers, into the mouth of their speaker. They expected to be able to use up the Book of Mormon upon the point of Adam's partaking of the forbidden fruit from the hand of Eve; but the answer that the woman was found in the transgression, and not the man, came so, quickly that it hushed them up at once, so that they could not argue further. Brother Orson Pratt whispered to brother Cordon the answer. Many of even these my sisters who are before me to-day have seen the wisdom that is in the Christian, world, while they have been, conversing with their former priests, and, have answered some little question that was a perfect mystery to a priest—a little question which they understood, and the priest did not, and have seen the priests thrown completely off their guard, become dizzy in their heads, and unable to continue the conversation. It is written in this Bible that the woman was found in the transgression, and not the man; and that plain doctrine has battled all the learning of the priests.