Women shouldn't study Gemara. It obscures the differences between the genders and leads to a decrease in God-fearing and mitzvah observance.Let's take this claim apart.
--- former Chief Rabbi Mordechai Eliyahu.
1 - Women shouldn't study Gemara: Why not? The idea that there's something wrong about women learning Oral Law is the opinion of R. Eliezer as quoted in the Gemara. He only states one opinion among three. "The Gemara" does not take sides between the three opinions. But for some reason (hmmmm... sexism?) the "tiflus" opinion is the one that's become famous.
In the old days many forces -sexism included - conspired to produce very few learned women. Many of those forces no longer obtain, so why should women sell themselves short? Out of sentiment? Out of nostalgia for forces that have passed into oblivion?
2 - It obscures the differences between the genders... Odd. I've know two or three gemarah learning girls. One was hotter then the next. Is this complaint of Rabbi Eliyahu's just a new variation on the old "smart girls are ugly" canard?
3 - It leads to a decrease in God-fearing and mitzvah observance: Has the Rabbi conducted a survey? It seems to me that a claim such as this can be defended empirically. If Rabbi Eliyahu has the data let him share. If he has no data, why is he putting forward the claim?
(FWIW, my own experience (and yes the sum of anecdotes aren't data) is that girl gemerah learners remain committed to mitzvot and continue fearing God; though some, unfortunately, come to embrace some apikorishe ideas. The reason? Perhaps because torah true types, like Rabbi Eliyahu, are too holy to teach woman, forcing those with a thirst for talmud leaning to study with kofrim in academic settings.)