I recently had a discussion during which the idea that women reason in a logical fashion was scoffed at, and not without reason. This discussion had involved what would be considered thoroughly illogical leaping to conclusions from an Aristotelian logical standpoint.
We are probably all familiar with the trope of, "Are you saying I'm fat?" In this trope, a woman suggests that a comment made by someone else which did not state that she was fat was indeed stating that she was fat. Another example might be a case in which someone tells a woman that she looks very nice today and she concludes that they don't think she looks nice most of the time. Of course, the person may find her very attractive every day and simply believe that she looks even prettier on that particular day for whatever reason.
There is no logical (or even empirical) necessity to the conclusion that the person does not think she looks nice most of the time. This is a distinctly different reasoning process than classical logical reasoning in either the formal or informal sense and we would probably dismiss it as fallacious in a formal philosophical context.
It is fairly widely recognized that on average men and women use disparate thought processes to make decisions about mate selection, sexual activity, and a variety of other activities. There is even a set of memes which make fun of various stereotypical thought processes found in men and women. And it is certainly appropriate to have those memes for both men and women; as human beings we all make cognitive errors, and our sex often influences the specific sorts of cognitive errors we are likely to make.
None of this is to suggest that there are not women who think more like the average man and men who think more like the average woman. Our behavioral traits exist on a spectrum and there will always be extreme outliers on the bell curves. And even within the average, men and women can learn to think more like the opposite sex with experience and practice. This is what should happen if we have healthy relationships with one another and attempt to deeply understand each other.
And either men or women can be trained enough in classical logic to use the kind of deductive and inductive reasoning which we would recognize as being valid, so we could not conclude that women are incapable of reason. Women reason quite effectively, though on average their goal in reasoning is somewhat different from the goal we would have in reasoning in a formal philosophical context.
Given what we know from evolutionary biology and psychology, it certainly makes sense that women would on average have a different goal in mind when reasoning because men and women have adopted somewhat different survival strategies in response to the biological differences between men and women. For women who are likely to be even more heavily dependent than men are on the tribe to protect them during periods of reduced physical capacity or incapacitation (as a normal function of biology), it would be vitally important to their survival to monitor the relative strengths of the various relationships they had developed with members of the tribe who provided that protection and assistance.
A great way to monitor the strengths of those relationships is to communicate an insecurity about how the other person views them, allowing the other person a chance to either affirm their regard for her or to agree that their perception of her is not as positive as she would like. And because it is much more costly to be wrong about having a strong relationship she can count on than it is to be wrong about having a weak relationship she cannot count on, it is quite rational from a risk aversion standpoint for the default assumption to be that the relationship is not as strong as she would like.
While the sort of reasoning which many make fun of as "woman logic" or "female logic" might not be a correct method for assessing the truth or falsity of any given individual proposition, it is a useful heuristic tool for managing risk with regard to the relationships upon which she relies for survival and quality of life for her and any dependents. Women on average may seem more insecure than men, but they have to deal with greater risks than men from a biological standpoint and it makes complete sense for their risk management strategy to account for that by taking greater measures to mitigate the likely effects of those risks.
I am generally of the opinion that women are quite good at the sort of reasoning they need for survival, just as men are quite good at the sort of reasoning they need for survival. And because we all make typical human cognitive errors, I have serious doubts that we would be justified in concluding that the reasoning of women is impaired in any important sense on average relative to the reasoning capacity of men.