The competence of women is unknown, however, in these cities since they are only taken in them for procreation and hence are placed at the service of their husbands and confined to procreation, upbringing, and suckling. This nullifies their [other] activities. Since women in these cities are not prepared with respect to any of the human virtues, they frequently resemble plants in these cities. Their being a burden upon the men in these cities is one of the causes of the poverty of these cities. This is because they are to be found there in double the number of men, while not understanding [through] their upbringing any of the necessary actions except for the few actions--like the art of spinning and weaving--that they undertake mostly at a time when they have need of them to make up for their lack of spending [power]. This is all self-evident. This being so--and it is clear from the case of the females that they are to share with the males in war and the rest [i.e., ruling--ES]--it is fitting that, in choosing them, we seek for those very natures that we sought for in men and that they should be trained in the same way through music and gymnastic. Ibn Rushd, Commentary on Plato's Republic, The First Treatise (p. 59 in Lerner's translation)
I am certainly not the first to notice that Ibn Rushd has proto-feminist tendencies (see here and here). They are developed (i) within a Platonic framework (recall) and (ii) they are offered despite the fact that he sometimes uses (not unlike Plato, in fact) feminine gender-stereotypes in negative ways. On (i): he is committed to the metaphysical idea that "the nature of men and women is of one kind." (58) Within the kind there is considerable heterogeneity (which underwrites specialization and the hierarchical division of labor within the city). But within each sex the distribution of talents is roughly equal between the sexes. (He allows that men are on average stronger than women, but he also notes that there are plenty of skills in which women excel men.) Given this equality, the best women are just as capable of ruling as the best men if they are properly educated/cultivated. This is a core commitment of what we may call Platonic feminism (recall also De Gournay).
The passage quoted above occurs when Ibn Rushd goes beyond Plato. He is explicitly introducing empirical considerations into the argument and, anticipating Hobbes (on the Amazonians [recall]), points to (semi) empirical examples of polities ruled by women-warriors including desert communities and "City of Women." There is a textual variant that goes 'inhabitants of deserts and frontier villages'--this is especially notable because it recalls the original Arab tribes and, also, suggests that Ibn Rushd senses a negative trade-off between civilized life and women's political activity (see here for more on this issue). The empirical evidence is then combined with a theoretically motivated counterfactual (based on his Platonic commitments about human nature).
For, it's quite clear that Ibn Rushd believes that if women would be given more opportunities and a better education they would be capable of contributing to civic life and economics of the polity. In fact, while we may wince at Ibn Rushd's 'women in these cities...frequently resemble plants,' the point he is making is that lack of opportunity and a certain form of domestication in the service of breeding genders women in ways that harms their intellects and the polities they inhabit. He then suggests (anticipating Thomas More) that if women would be allowed to contribute to economic life, the polity would be enriched. The argument is simple: allowing women to participate would give a one-off huge boost to output (he kind of implies it would be 200%), and would turn them from passive consumers into productive agents. (Presumably due to polygamy, women outnumber men.) The argument is quite general and applies to all women not just to potential guardians (who are unproductive, after all).
Of course, Ibn Rushd himself does not think economic enrichment is the aim of a virtuous city. This is why his argument is so notable. He is explaining to his compatriots, who do think that pleasure and wealth are true ends, that if they understood their own self-interest better they would engage in a program of female emancipation. It would be interesting to explore the roots of arguments that appeal to the very idea of self-interest properly understood in the service of an ameliorative program that itself is not taken to be best.
I close with an observation which shows Ibn Rushd's remarkable sensitivity to how empirical evidence needs to be handled. Ibn Rushd also provides an error theory for why some religious traditions/Laws [the Hebrew has Tora, presumably he is referring to Sharia], fail to recognize women's emancipatory potential. The passage is fascinating because it shows how Ibn Rushd (again anticipating Thomas More) is willing to historicize religious law:
since some women are formed with eminence and praiseworthy dispositions, it is not impossible that there be philosophers and rulers among them. Since it was thought that this class existed only infrequently among them, some [religious] Laws ruled out women's being priests--i,e,m the high priesthood. (58)
These religious laws have the correct metaphysics, but (the authors of these) misinterpret the empirical evidence. They recognize that men and women belong to the same kind, but falsely assume -- based on empirical evidence -- that the distribution of qualities among women is skewed toward lack of talent and skill. That is, these authors do not recognize that empirical evidence of human affairs can exhibit great status quo bias toward the possibilities permitted by institutional arrangements.