The argument you are attacking here is based on two false premises, and you do a good job of attacking the first premise i.e. that human society in the past was patriarchal because of the need to hunt. But even if that were true, it doesn't support the inference that society should remain patriarchal today. Evolution operates by exapting old skills into new contexts, and the only creatures who survive the evolutionary gauntlet are those who can adapt as environments change. Agriculture and commerce require cooperation, and competition only becomes necessary in a few contexts. We have treated competition as if it were the essential virtue of society, but that belief has always been a very bad fit for the way we actually live. If we continue to try to conquer nature--to behave like predators from whom all of nature is our prey--we will destroy all of nature and ourselves with it.