snub-nosedmonkey, you misunderstood what the article is claiming. Let me paraphrase:

For example, it was long thought that brain size determined intelligence or competency in certain skills - women's brains (or certain parts thereof) are often smaller than a man's, thus this "shows she is competent in women's things but not in "man's things"." In more modern studies this has been debunked as brain size is not strictly relegated to sex (just like how many men are tall, but not all of them) and that size of the brain does not affect some's intelligence.

So this paragraph here does not deny that the average brain of a man and a woman is different, it instead challenges the idea that brains can be gendered. To reduce confusion here, there is no proven part of your brain that makes you feel "female" and no part of your brain that makes you feel "male". If you read the articles linked in the original post, it also shows that your life experiences (keeping in mind that both men and women often live lives relegated to their gender roles) and what you use your brain for can increase the size of that area of the brain as well as the connections.

Currently there is no solid study that actually proves that a brain sex can be proven, at most only minimal differences have been found and no individually fully conforms to either. A lot of brain studies you'll find are extension or part of "pop science" and research cherry picking, when done with a large sample size like this study here (6,000 people), the issues become apparent with the claim: https://www.sciencedaily.com/releases/2015/10/151029185544.htm

"Many people believe there is such a thing as a 'male brain' and a 'female brain,'" Dr. Eliot said. "But when you look beyond the popularized studies -- at collections of all the data -- you often find that the differences are minimal."

Meta-analyses by other investigators have also disproved other purported sex differences in the brain, Dr. Eliot noted. There is no difference in the size of the corpus callosum, white matter that allows the two sides of the brain to communicate, nor do men and women differ in the way their left and right hemispheres process language.

It's not a good principle to bring the sex differences in primates and other animals because human beings do not grow up and act like other animals - some animals have large brain differences and more instinct reliant, others aren't as much. If we want to study human brains it has to be human studies.

Male and female hormones and their production as you mentioned in your comment here - is something complete separate and are actually produced by other organs in your body (sex) or hormone supplements, your brain is affected by said hormones indeed but not the producer of them.