the average man (most men) dont have more power than the average women.
I actually disagree on this.
Money is power. Men are stereotypically the primary household earner. Women in those relationships rely on the men to provide an income, and men's ability to take that away gives them power. Obviously, this isn't strictly a good thing for the guy, since it comes with stress for him to provide, but it does skew power in the relationship.
Consider a normal distribution, with the x axis being "strength" and the y axis being "number of people" - lots of people are medium strong, few people are very strong or very weak. If you split that into two - one for men and one for women, and compare the top 1% strongest men and women, the men would be stronger. Since it's a normal distribution, it also shows that the average man is stronger than the average woman. There are still many, many women that are stronger than the average guy, but as a population men are stronger.
I submit that "power" follows a normal distribution as well. I'm sure we agree that the top 1% of men are more powerful than the top 1% of women, so it would follow that the average man would be more powerful than the average woman.