There is no discrete difference between male and female brains, just as there is no discrete difference between male and female. The difference arises when we look at trends, majorities, and averages. Just as the majority of the population can be identified as ‘biologically male’ or ‘biologically female’ with reference to reproductive organs and hormones. Nearly all aspects of human behavior, biology, etc. occur on a spectrum. If we look at the distribution of ‘biologically male’ and ‘biologically female’ for any specific trait (ex. height), it is highly likely that the average male and the average female will not fall on the same place on the spectrum. But it is also almost certain that there will be some overlap of the distributions.
So it’s not really correct to say that ‘male and female brains are fundamentally different’ so much as it is to say ‘the average male brain and the average female brain are very often different.’
In fact, Prof. Cahill even says so in his article in Quillette: “So are female and male brains the same or different? We now know that the correct answer is “yes”: They are the same or similar on average in many respects, and they are different, a little to a lot, on average in many other respects”
So we absolutely do need to appropriately represent females in scientific studies, because on average, their results may be quite different from males.
I think too, that some of the anger from feminists comes from when scientists try to establish ‘fundamental differences’ based on behaviors or illnesses (such as depression or anxiety) when our behaviors are so dependent on the social structure in which we were raised.
For example, depression and anxiety may be seen more often in women not because our brains are different, but because of the societal pressures under which we operate. On the same token, it could be that men are underdiagnosed for depression and anxiety because our society has established ‘appropriate behaviors’ for them as well.
With regards to the animal/mammalian studies that Prof. Cahill argues are so important, results, especially behavioral/cognitive results, can be biased, often unconsciously, by the humans conducting the study. In addition, our closest mammalian relatives also exist in complex social systems. So you cannot argue that behavior X seen in female humans must be biological and not social because behavior X can also be seen in female apes. And I would argue that while behavioral studies on smaller mammals can be important and useful, we should be very hesitant to apply their findings broadly to explain human behavior.