I asked two women and one man. One woman was my missionary/teacher, the other was a mother whose family drove me every Sunday morning. The missionary (her hand-written lesson notes are stored safely in a box for sentimental reasons) gave a vague, somewhat robotic (if I may) answer about God-appointed authority. The mother did the same, but afterward in privacy elaborated on her answer by saying that once I enter the Temple, I'll see that there's more to it.
The man essentially said the church doesn't have priestesses because women are too busy with the important job of mother. His wife was the "home manager".