Being [called] a Rabbi can mean:
- Someone respectful in the Jewish community and be elected to run the community: a female Rebbetzin can be very respectful and can be elected to run the community based on Hilchos Shutfim (partnership).
- Being knowledgeable in Judaic sources and give answers: women can be very knowledgable (so can Google).
- Passing exams for Rabbanut: of course, see the previous point
- Having some guiding Ruach Hakodesh (being an Admo"R): unless a woman is a known prophet she can't have the necessary "closeness" to Hashem that specifically comes from studying the Torah for its sake (not for knowledge). As women lack that Mitzvah they lack that "ability", and therefore can't reach the necessary levels of Ruach Hakodesh.
- Being a Posek: different movements see it differently - those who follow #2 and #3 - a woman can be a Posek, those who follow #4 they can't.
We address this issue of female Rabbis a bit differently - it is not a matter of permitted or forbidden it is a matter of validity. For example, it is not "forbidden" for a woman to witness an event, just her testimony is not valid. So there's no problem with women being called Rabbis/Rebbetzins or whatnot, the question is about the validity of their deeds.
For example, (some say that) if a Rabbi Posek that a chicken is Kosher or a stain is pure, he turns it into the reality of Kosher, but if I say it's Kosher, I don't set the reality and I might make others fail. So the question is "what's needed for a woman to reach that level of validity of her verdicts. It appears, that similarly to judges or witnesses, the Torah does not provide an option for a woman to set the reality. Therefore a woman can not become "that sort of" a Rabbi.