I recently listened to a radio show where the participants discussed, “What can a deacon do that the non-ordained cannot?” I don’t think they ever came up with an answer that was satisfying. It seems to me that none of the tasks that are routinely assigned to deacons actually require the sacramental order of Deacon. I propose that the unique power of the sacramental diaconate is that only a deacon can be ordained priest. Seeing as the diaconate is what bestows upon someone the capacity to be ordained a priest, and women can’t be ordained priests, women can’t be ordained as deacons. QED.
Note: I grant that there was an office of “deaconess” in the early Church. Like the offices of widow, nun, abbess, and hermitess, it wasn’t a sacramental order.