M. Russell Ballard suggests that while the Lord designated men as holders of the Priesthood, it has not been revealed "why He has organized His Church as He has."
M. Russell Ballard, "Let Us Think Straight," BYU Speeches, August 28, 2013, accessed June 27, 2023
Why are men ordained to priesthood offices and not women? President Gordon B. Hinckley explained that it was the Lord, not man, “who designated that men in His Church should hold the priesthood” and that it was also the Lord who endowed women with “capabilities to round out this great and marvelous organization, which is the Church and kingdom of God” (“Women of the Church,” Ensign, November 1996, 70). When all is said and done, the Lord has not revealed why He has organized His Church as He has.