Proof of females and males being different comes from my own experience.
Studies I've read show that male traits (when the second trimester hormones initialize the fetus brain) are mostly on the left hemisphere of the brain, and female traits gather on the left side.
In my case, I was conceived a few months after my brother so acquired his male hormones as well as my natural female hormones, resulting in two gender personalities. I also acquired dyslexia, a male trait, and the lack of communication between the two hemispheres resulted in much confusion for me.
Objects would disappear and reappear days later in weird places. When I was growing up, people often often yelled that they had told me something only that morning, and since I had no memory of it, I assumed they were lying. I thought my world seemed nuts at times, and coped the best I could.
In 2013, I found out I was transmale, and began to officially recognized my male side, naming him Raell. I eventually became aware that I could look through the eyes of either my male or female side. But one gender mode side didn't acknowledge the other, or fully remember what happened when in the other mode. When in male mode, I'd deny I had a female side, and the reverse when in female mode. Each side had different tastes in music, books, world view, reactions, likes and dislikes.
My male side is easy-going, fun-loving, lives in the moment, loves everyone, loves all sports, loves to gamble (tiny amounts) on just about any contest, thinks women are hot (this despite my being asexual). He'd swing around to ogle someone, but any follow-up sexual thoughts would quickly shut down-no doubt by my female side waking up and nixing it.
Strangely, many "bro" characteristics were somehow hardwired in..wanting to scratch non-existent "crotch" when I first got up, being totally loyal to my male pals, sometimes feeling a ghost "erection" when seeing a beautiful girl, loving action movies, some extreme sports, laughing at slapstick humor, sympathizing with the man's perspective.
My female side is critical, picky, second-guessing, obsessive, freaks out, an obsessive bird photographer, thinks men are morons, holds grudges, a perfectionist, loves art, designing clothes, likes only a few people, a bit of a snob, religious, constantly critical of my male side, who could do nothing right in her eyes.
To escape her relentless criticism and worrying, I chose to remain as much as possible in "male mode."
A few years ago I took a Thai evergreen herb for back pain, and strangely, the herb seemed to cure dyslexia and blended my two gender personalities.
Suddenly, when something seemed to disappear, I'd then remember where I put it. Things hadn't been vanishing after all..I had been the one who moved them. Now when people said they'd told me something earlier, I could then remember it. I no longer have to suppress my male side's tendency to notice women, and consider myself a more blended personality, now enjoying the interests of both at the same time.