That women deacons or women cardinals are a possibility in the Catholic Church is admitted in even orthodox circles. The priesthood is closed to them, but depending on how you nuance it, women could potentially be deacons or cardinals:
(1) Women Deacons: Two possibilities: (A) Non-ordained “Deaconess” may not be an ordained role on par with the ordained deacon of Holy Orders, yet the early church had some sense of women deacons. (B) Ordained Deaconess is less likely, but even the ordained deacon of Holy Orders is not a priest. So the reasons are not theologically the same, if women are to be closed off from the permanent diaconate.
(2) Women Cardinals: The basis of women cardinals comes from the reality that Cardinals are not inherently ordained, though that is a modern requirement. In the past, they could be lay. The essential reason role of a Cardinal, as a lay person, would be to be an advisor to the Pope.
- Woman Deacon/“Deaconess”
- Woman Cardinal
- Both equally likely
- Both highly unlikely