If you just want to study the original rabbinic sources on gender and Torah reading, and to reach your own conclusions, you can find all the material on the Podcast and Sources page of this site, fully-translated, together with links to the explanatory podcast itself.

For those who are interested in more modern writing on gender and Torah reading, the easiest academic introduction to the subject was written by Rabbi Daniel Sperber in 2002 and is posted here. I have written a shorter, popular article for the Jewish Chronicle which is here.
Tradition?
Many opponents of women’s Torah reading argue that, while it may be permitted in theory, it militates against long-standing Jewish tradition. Sometimes they try to make this position sound more authentic by using the Hebrew word “masorah” rather than the English “tradition”.
This position will not stand scrutiny: the authentic Jewish tradition carries many diverse voices, of which a significant number would be considered “feminist” today. I have written in the Jewish Chronicle here about feminist voices in the classic rabbinic tradition, here about gender equality in the rabbinic rulings related to the life of the synagogue, and here about a classic rabbinic debate on the subject of women’s education.
Other opponents of women’s Torah reading simply argue that yesterday’s and today’s practice of not calling women to the Torah cannot be changed. This position too does not stand scrutiny: it fails to recognise the extraordinary creativity, innovation and flexibility of the rabbinic tradition and I have written about these subjects in the Jewish Chronicle here.
Scholarly Publications
A longer, scholarly article about women’s Torah reading, by Rabbi Mendel Shapiro, is posted here. Rabbi Yehuda Henkin, a leading authority on Jewish law from Israel, has written a response to Rabbi Shapiro, in which he accepts most of Rabbi Shapiro’s arguments but opposes women’s Torah reading because it is “outside the consensus”. It is posted here.
Rabbi Shlomo Riskin, an important community leader and educator based in Efrat, in Israel, has also composed a response to Rabbi Mendel Shapiro. His arguments are posted here. Subsequently, Rabbi Shapiro has written a reply to Rabbi Riskin’s challenges which is posted here. Reading this exchange was a “light-bulb moment” for me (see Page 25 of the pdf).
The most well-known attack on women’s Torah reading was published in the American rabbinic journal “Tradition” in 2014 by the two Rabbis Frimer. While it is posted here, it is not for the faint-hearted: it runs to 62 pages, together with another 112 pages of foot-notes, and is written in an impenetrable style that most readers will find difficult to navigate.
The overwhelming majority of the rabbinic sources that the Frimers claim to bring in support of their key conclusions are mis-represented. My own response to the Frimers, also published in “Tradition” and posted here, makes this clear, as well as outlining the Frimers’ arguments more succinctly than they do themselves.
Rabbi Yehuda Henkin’s response to the Frimers, in “Tradition”, is posted here and hints at the same issues.