Tridentinus, I speak only to the proven unhealthy environment/ circumstance of "Secret Men-Only Societies" which give cover to men of perverse intentions - a reality that exists today as in the past. I speak as a 57-year member of the Knights of Columbus.
It surely seems inappropriate for religion/ churches to facilitate in any way male over-reach and put-down of women.
Church's denial of the Ordination of women to Priesthood fuels male self-arrogation. As an eleven-year seminarian to the priesthood in a Religious Order, i have some personal experience; and as a father of six daughters, i have reason to speak in interests of women; so i do.