I begin by saying that my name is often written as "Rabbi Ally Ehrman" which sounds very much like the name of woman rabbi, so I am biased from the start in favor....:-)
First the pure halachic issue: Is it permitted according to our classical sources for a woman to be a rabbi? The answer is unequivocal - there is a difference of opinion. Some sources seem to say that it is permitted [the Chinuch, Birkei Yosef and others] while others differ [see here].
I don't think that the issue is purely halachic. There are more basic issues involved.
1] What does it mean to be a posek? It means that one has sufficient mastery of all of the relevant sources to render halachic decisions. Let us take hilchos niddah for example. Anyone can learn and teach the halachos that are already written in the sefarim. That is what kallah teachers do and ALL kallah teachers are female. But none of them are qualified to pasken i.e. to decide questions that are not explicit in the books. Here is gets complicated. Hilchos niddah are filled with questions that relate to principals of chazakos [assumptions] and sfeikos [doubts]. The answers are rarely "local" and open and shut. One must span the length and breadth of many of the most complex sugyos in Shas. Some are in maseches krissus. Is there a women alive who has learned maseches krissus with all of the relevant commentaries? In order to decide questions in hilchos niddah one must be an expert in the sefer Shev Shmatsa which is a classic in the field. Is there a woman alive who is an expert in the Shmatsa? Is there a woman alive who has ever went through the Shmatsa even once [if she wants though she can listen to my shiurim and read my many articles on the topic. Sorry - for the plug...]?
So how can she decide such questions?? This does not mean that women aren't intelligent enough to understand. I have a daughter who has a better gemara head than just about any male I know. A genius. I ask very difficult questions at the shabbos table and almost every time she answers on the spot what some great Roshei Yeshiva answered. This is not because she has been through Shas but because she is a genius בלי עין הרע!!!! So I am not claiming that women by nature lack the necessary intelligence. But in order to be a posek one must spend yeeeaaarssss of intense 12 plus hours a day of study. Women, because of familial and other obligations, just can't do that. [Incidentally - she is interested in being a rabbi like I am interested in becoming a ballerina].
Interesting. How does one become a posek? Peer review. One writes a sefer and others read it and if the sefer passes the test of their scrutinizing eyes and sharp criticism then he takes his place on the list of great rabbis. I know one well known rabbi in a prominent position who wrote a sefer that a 14 year old could have written. This will effectively prevent him from ever being taken seriously [he isn't]. In contrast, open up an Igros Moshe and you see why Rav Moshe is considered a gadol. In the last 40 odd years, since the feminist revolution began, not ONE sefer in halacha or gemara has been written by a women that has gained respectability. I don't even know of such a book has been written at all. She'elot U'tshuvot Igrot Miriam. Never seen it. [All the "Miriams" reading this - a project for you!!:-)]
My conclusion - women [in most cases] aren't really interested in being poskot!:-) They see their roles in other capacities. Wives!! Mothers!! Yayyyyyy mommiesssss!!! Nurses! Doctors! Kindergarten teachers! Therapy [ot, st etc.]!! Many great jobs for our holy women. We have tremendous respect and reverence for our women. But we don't need "poskot". The men fulfill that role, just as they have been doing for the last 3,300 years. If klal yisrael doesn't need it and the women aren't so inclined - then why have it?? If a women wants - let her become an expert at Tanach [as some women are] and teach that!:-)
Another point made by Rav Schachter here. Tznius. Some people say that women are part of the working world anyway, so why is a woman rabbi any more a breach of tznius than other jobs. The answer is that having a woman leader guiding a community puts her at the center of attention. According to our tradition a woman shouldn't be the center of attention. Some people don't like this and want complete equality between men and women. If men can be the center of attention then so should women. Herein lies the problem. Sure an assertion is essentially saying that our tradition should be altered. I can't subscribe to such an approach [or to Sports Illustrated for that matter:-)]. If we want to stay within the confines of our tradition then tznius is part of that. A woman getting up and giving a drasha in front of 300 men is not so simple to justify "tzniusly".
Last point: Slippery slope. Once this barrier is broken what is next?
There is more to say but I will leave it here. Please show me how I am wrong....