Rings & Books
There is the question of the innate differences of biology, which may involve thinking, as noted by
@Hanover, and the role of cultural assumptions and the dynamics of power relationships. It may be complicated.
Mary Midgely's comment about the way women don't put each other down, may be about female psychology. Or, it may be about the situation of females in philosophy and their precarious situation in a male dominated profession in the institution of philosophy at the time, as if being there itself was a 'privilege' and a shared respect for one another as it may be problematic to argue that females never put other females down, such as in situations where they are competing against one another.
The dynamics of institutions involves power relationships and ideas about gender. Even recently, I read of a situation in the news in which a woman applied for a high position in an organisation and was rejected. When she sought feedback, she was told that the reason why she had not been given the job she was told that it was because she had not 'put enough effort into her appearance'. The woman claimed that what this amounted to was she had not worn make up. It reminded me of how the most successful woman I knew in philosophy, a professor and well known figure in medical ethics, who was a tutor, was adored by male students for her sexual attractiveness. I won't name her, just in case she were to read this online forum, but I wonder if she would have risen to fame if she had not been so attractive.
What I am arguing is that gender relationships are not simply about misogyny but about stereotypes. In the twentieth first century the situation may have changed to the point where there is more bias against males in some contexts. For example, what I have found when looking for accommodation is that so many adverts say, 'females only', which may mean some difficulty for males in finding 'a room of one's own'.