The Church in its teaching notes that Jesus disregarded the culture when He chose, which indicates that his selection of men only was conscious. In this case the practice is not a tradition but part of the Tradition, the infallible ordinary magisterium constantly taught and practiced without exception.

This is why we can only celebrate the Eucharist with bread of wheat, not rice, not barley, not corn, but the celebrant does not have to wear sandals and speak Aramaic.