No, that's not it.
Sorry but you are wrong. In old english 'man' meant person without any gender specification because 'wer' meant male human where is where "werewolf" comes from: literally "male person-wolf". However because we started to use the word 'man' to mean male human this interpretation has now been retroactively applied to words which were derived when the meaning was gender neutral.
And for what it's worth, for all of the complaints given about the US, the US is perhaps one of the least male-dominated societies out there.
Seriously? So how many female government leaders have you had? Your congress has under 20% women compared to ~25% for Canada, UK and Australia and 30% for New Zealand. Even Saudia Arabia has a 1% higher proportion of women in its national parliament than the US. In many European countries the ratio is in the upper thirties to forty percent.