There have been many psychological studies on this topic over the many years. Whether one is studying personality or intellectual traits between males and females, the professional roles they have or seek out, or roles within the family, there is huge amount of overlap. So, when someone begins claiming that both genders can do things equally, this would be more, or less, true for 80% or so of the population. However, when we start talking about the extremes, the 10% of females on one end of the spectrum, or 10% of males on the other end of the spectrum, the differences are extreme. There's clear reasons for male and female sports, because the extremes make it quite apparent. When we start talking about "the patriarchy" we have to keep in mind, it's not males, in general, but rather the 0.01% of hyper-extreme performers. Given the billions of people in this world, 0.01% means that people can come up of many, many examples of old, white men that are multi-billionaires that seemingly "rule the world" and create these huge income disparities that people get pissed off about. The reality is that the other 99.99% of males, clearly are not included in this group, and for the most part, contribute to the vast majority of suicides, killed in war, killed on the job, do most of the hard, physical labor in the worst of environmental conditions, most likely to lose their children, homes, and money due to divorce, have worse health, lower life expectancy, and the list goes on and on. The statistics very clearly do not support the myth of males having some sort of advantage, in fact, quite the opposite. The patriarchy only exists for the tiniest fraction of us. Furthermore, now-a-days, there are many, many large corporations with female CEOs.
Gender roles have historically been, more or less, a result of this idea that the "father and husband shall provide" and the "mother and wife shall raise the children and run the household". Even now-a-days, despite the fact that women are more educated and are heavily in the workforce, men still are expected to provide and do the sorts of jobs that build our infrastructure and modern conveniences. Overwhelmingly, men build things. Most women are not signing up for these physically demanding professions. Many women are often choosing not to get married nor have children, and would rather focus upon their careers in other areas. To each, their own. Obviously, our society is experiencing a transition in our traditional roles, not better, nor worse, per se, but different.