Why do you think the labor force participation rate of men is higher than that of women in the United States? Why has the labor force participation rate of women been increasing so dramatically? What are some of the reasons for variation in labor force participation rates of different countries?
All of the things that you are asking about here are caused mainly by societal and cultural norms. They are caused by what society thinks is right for men and women to do and by changes in those attitudes.
It should be said that there is one other reason that is at play here. That is the amount of physical strength needed for the jobs that make up the bulk of employment in a given economy. In the past, many more jobs required physical strength greater than that possessed by women of the time. This made it harder for women to work. Therefore, men had higher labor force participation rates. In advanced economies, jobs no longer tend to require as much physical strength. This has led to increasing rates of participation in the labor market by women. In some countries, jobs still require greater strength, making it less likely that women will be in the labor force in those countries.
However, this factor is not nearly as important as culture, particularly recently. In the last few decades, we have experienced something of a revolution in our attitudes about sex roles. Where we once thought almost universally that women should stay home and take care of the kids, we now feel that it is right for women to have careers. This change has caused women’s labor force participation to increase dramatically. Men still have higher rates of labor force participation largely because we still expect men to work but think that it is okay for women to be homemakers. As long as that attitude persists, we will have higher participation by men.
In some other countries, these attitudes have not changed nearly as much. Japan is a perfect example of this. Japanese women do not participate in the labor force nearly as much as American women. This is largely because their culture and society expect that they will stop working when they get married.
Thus, the most important cause of the things you mention in this question is the way that society assigns sex roles.