A tad off topic, but I notice that women can do pretty much the same thing in the RC that they can in nonRC.
The only exception I can think of is give a lecture/study on Sunday during main services. Other than that there's nothing I can think of that women can do in other Churches that they can't in RC.
Women cannot be deacons.
Women cannot perform the Sacraments, including the Holy Sacrifice of the Mass which includes the Holy Eucharist.
Women cannot be bishops.
Nor can I go to a woman to receive the Sacrment of Reconciliation, Baptism, Confirmation, Annointing of the Sick, Holy Orders or Matrimony.
And you are right Catholic women are not allowed to give a homily -- only the ordained deacon or priest.