A rabbi is generally in a very public position. One of his tasks is to lead the Torah learning with the congregation's men, which is supposed to be one of their principal occupations aside from earning a living. The majority of a rabbi's time is spent with men for this reason, and his role in the synagogue itself dictates that he be in the mens' section.
Men and women who are not spouses, or father/daughter or mother/son are not supposed to touch, as a gesture of modesty. Observant Jews are very into modesty, a very rare commodity these days of everybody grabbing everybody and anything. Obviously, a woman "rabbi" would be in the forefront of a synagogue's activity, which is not considered very modest for a woman (she has her own tasks for which men are not as suited). Neither would sitting and learning Torah with a bunch of men.
There certainly are women's Torah learning groups and very learned women who have authored scholarly texts, but their main task is molding the next generation into fine human beings. I know Orthodox women doctors, lawyers, scientists, administrators, accountants, you name it--but they would all agree that their most important work is raising their children to be G-d-fearing fine human beings.
Lynn Gottlieb is almost certainly the product of a non-religious ultra liberal home where they knew more about "civil rights" than Judaism. Therefore, she is a misguided person who really should not represent herself as a "rabbi". Her Jewish inborn compassion is unfortunately misdirected at Palestinian haters rather than her own people. Her intellectual gifts, such as they are, are misdirected to helping the enemies of Jews and of the U.S. One should pity her as a product of such a spiritually deficient home.
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Most likely she was born into an ultra liberal Jewish home, her parents might have been commies or ex-commies. She is a publicity hound witch who gets publicity by hanging out with Ahmadinejad and other Muslims who want to destroy Israel. I laughed a few years ago when one of those Neturei Karta idiots (and his family) wee hounded out of the Jewish neighborhood they lived in. This came after one of their visits to Iran to play footsie with Ahmadinejad