Neither Plato nor medieval Islamic philosopher are particularly known for their feminism, though apparently in the case of Averroes (Ibn Rushd), the two seem to have combined to serve such a cause. This is pointed out by E. I. J. Rosenthal in his work on Averroes’s theory of politics:
Ibn Rushd's critical attitude to State and Society of his time is also shown in his outspoken pronouncement on women and their status in contemporary Islam. It is also an interesting application of Plato's ideas about the equality of women as far as civic duties are concerned. The relevant passages are found in the first treatise of the Commentary (xxv, 6-10). It is for our purpose sufficient to quote paragraphs 9 and 10-Averroes' application to his own time and place:
Yet, in these states the ability of women is not known, only because they are being taken for procreation alone therein. They are therefore placed at the service of their husbands and [relegated] to the position of procreation, for rearing and [breast] feeding. But this undoes their [other] activities. Because women in these states are not being fitted for any of the human virtues it often happens that they resemble plants. That they are a burden upon the men in these states is one of the reasons for the poverty of these states. For, they are found in them in twice the number of men while at the same time they do not support any (or: carry on most) of the necessary [essential] activities, except for a few, which they undertake mostly at a time when they are obliged to make up their want of funds, like spinning and weaving. All this is self-evident.
This pronouncement runs counter to Islamic teaching and practice and is the more remarkable since it is made by an orthodox member of the Muslim community which was ruled by the amir al-mu'minin, and moreover by a practising lawyer steeped in fiqh. He openly attacks their way of life as the result of the official attitude. It is clear that Plato's ideas must have drawn Averroes' attention to the wastage of human labour so detrimental to the State, and led him to advocate a reversal of orthodox Muslim policy. (“The Place of Politics in the Thought of Ibn Rushd” pg. 251-252)
I would add that this view of women is distinct from that of the Jewish thinker Maimonides with whom Averroes is often compared. Throughout Maimonides' work he used women as a term of derision and he is a major source in Jewish law for stringencies on the role of women in public life. To be fair to Maimonides he, as with most "misogynistic" philosophers, possessed a general all round contempt for human beings as a whole. For Maimonides, women had all the flaws of the rest of the human race without the redeeming quality of having produced a least a few great rationalist thinkers. Averroes shared Maimonides' contempt for human beings and like him distinguished between the exoteric claims which can be revealed to the masses and the esoteric truths which can only be understood by the philosophical elites. In this they were both following the political philosophy of Plato's Republic. Yet Averroes supported women taking on public roles and believed them capable or rational.
So what pushes a person to ideological misogyny?