Goign back to the beginning of the discussion...
Broken, the argument above is simply not true, specially the bolded "because". Yes, if you live in a society where a given group has advantages, that group could take more risks (more on that later). But there is a thing called neuroscience, and also neuropsychology. Those are stablished scientific fields, with close to a century of data. There is no controversy for them: men take more risks, by nature. They even know which specific parts of the brain are responsible for what. They not only know this, they know it in detail, it is part of a much larger body of knowledge.
Of course that this is on average. You will find men extremely risk adverse, and you will find women with high appetitte for risk. But, on average, men take more risks. Then, on average, men pay the price for those risks more often, but also reap the rewards. You see those effects even in extremeley progressive (I hate that term) societies. There is not mcuh room for debate here.
As for patriarchy... IMO most of the time this term is misused. Go back mere 100 years in history and 95% of humankind still lived in a world were physical strenght is the trump card. The further back you go, the more this is true. Obviously societies would gravitate around men, which, on average, are stronger than womem, and on average again, more aggressive. People speak of patriarchy as some sort of conspiracy theory, some cult of men in funny clothes conspiring to stay in power. Nothing good or useful, nothing that can actually solve any real world problem will ever come out of that way of thinking.