Rav Kook expands on his views on the difference between men and women - that he stated regarding voting rights - regarding Torah learning and yeshiva. click here. He asserts that textual learning is only needed by men who have been contaminated by the outside culture. The cure is a constant dose of text based study. He likens the yeshiva to a hospital where this cure is applied. Women on the other hand have been sheltered in the home from the outside culture and are not contaminated. In addition because they have extra binah - they don't need textual studies as an antidote as men do. In fact textual studies are harmful to their spirituality. He cites the Rambam who notes that teaching women the Oral Torah is teaching them immorality. The following excerpt is from Dr. Avinoam Rozenak's on Rav Kook (pages 251-252) This letter which had never before been published was written by Rav Kook to his son and his older daughter Freida Chana (20th of Shevat 5667). The translation is entirely mine including the parenthetical notes of Dr. Rosenak.
The fundamental distinction, my precious daughter, between the soul of woman and the soul of man is only in relation to the necessity of intellectual study. Book are not in themselves natural sustenance for the spirit of man. [...] In fact the best of books [...] are only medicine to cure a man who has been sick for years. [In contrast] the healthy inner emotions which are produced from a pure nature by means of a chinuch (training) which is not destructive – are all that is needed to instruct a man as to that which is sufficient. [Cultural education, book learning and intellectualism are all consequences of sin and degradation – A Rosenak]
Man today has become seriously degraded and his actions are perverted and life in general is debased. [The ills of the material culture have struck man and therefore it is difficult for him to conduct his life properly and therefore he seeks] doctors and cures that are produced from studies of books. [In fact we have descended] to the unfortunate condition that we are forced to imprison our beloved children who are still fresh with the dew of their childhood – for many hours every day in the school room and to bind them to books and to text. This is comparable to requiring a sick person to be hospitalized and confined to bed in a hospital room. The child is carefully detained with strict supervision in order to provide him with the cure of study.
G‑d acted justly with the world in that He gave women a greater measure of understanding (binah) than He gave men. This is manifest in the fact that her basic intuitions are much deeper than a man. This is so even though they don’t seem to be from how they are expressed.[A woman exists in a different plane of realןtiy than a man. She has no need for the artificial framework of study and intellectual striving which supports the man A. Rosenak]. There is no absolutely no benefit for the woman of valor to be involved in the workings of the world leaders and kings or their cruel wars – which also add many chapters in books. [Involvement in this world of man can only lead to her destruction and degradation A. Rosenak] And it in no small measure injects in their lives the filth of murder and hatred of others that causes the light of life to be darkened. That is why the woman of valor is exempt from this catastrophe. She was created to look after the running of her house and to offer aid to the poor and indigent as well as to make sure her household was properly taken care of. [...] These tasks she fulfills are beautiful and pleasant and sweet smelling to those with understanding as well as inherently holy - and they are natural and wholesome in every aspect.
[In this idealized image, a woman could theoretically develop her full potential without any formal education at all. However with the degradation of the generations a woman has increasing needs for formal education. Nevertheless it is prohibited for a woman to exchange her world for that of a man A. Rosenak]. G‑d forbid for a refined Jewish girl who is destined to be a true woman of valor and even more so to be a daughter of Israel. [...] to exchange her living world for the artificial world of books and her wholesome food for medicinal chemicals The catastrophe of Europe which also imprisoned its daughters in a prison known as school [...] was the cause of producing generations of women who were weak in spirituality.
[These circumstances are the cause that women] have forgotten their true value. [Her parents for various reasons] seek only book learning in a fixed framework and to have her bound to a school room – to a hospital. And it is equivalent to teaching her what Chazal describe as immorality (tiflos). [Just as there is a chasm between Jews and the nations of the world there is also a significant difference between women and men. In these two cases, the distinction is inherent. Not everything in the nations of the world is positive. However in the end, the world must act in according with the Torah. Everything depends on the degree of connection that Jews have to their sources in the Torah and their implementation in the land of Israel. A. Rosenak]