The characteristics of the family environment that are most likely to affect gender roles are the roles played by the parents of each sex. These parents are likely to be the most influential role models when it comes to socializing their children into a given gender role.
When we are children, we learn how we are supposed to behave given the sex that we are. We learn what our society expects of boys and what it expects of girls. Much of this process of socialization takes place within our family.
Within our family, the strongest agent of socialization in terms of our gender roles is our parents. When we watch our parents, we get cues that show us what is expected of people of each sex in our society. We learn how adults of each sex are supposed to behave in a variety of situations. This is likely to shape our own views of what it means to be male or female.
This does not mean that we will automatically replicate our parents’ gender roles. We may observe our parents and decide that we do not like some or all of their gendered behaviors. However, the fact remains that their behaviors will influence us in some way.
Thus, we can say that parental gender roles are the family characteristic that is most likely to reinforce traditional or nontraditional gender roles in us.
The above response is spot on, since we all have a natural inclination to identify with the parent of our own sex and replicate what that parent's role has been in the household and in society. Traditionally, in most cultures, that has included males working outside the home to bring in earnings, and women working within the home, to take care of food preparation, cleaning, and child-rearing. Little girls saw mother cooking and concluded that was what they would do when they grew up, while little boys saw their fathers go out to work every day and followed that pattern.
Today, all of this is in flux, with more women than ever before working outside the home, comprising now, I think, more than 50% of the workforce, and with more and more stay-at-home dads doing the cooking, cleaning, and child-rearing. This implies that in fewer and fewer instances will the traditional gender roles be carried on into the future. Little girls will be more likely to see their mothers working outside the home, and little boys will see more dads doing the diaper changing and making dinner. And of course, we are also seeing more and more households in which both parents work and to some degree share equal responsibility for maintaining the household. Whether or not we ever reach a point at which male and female children are influenced "equally" to want to do both remains to be seen, since, in addition to "nurture," we do not fully know what part "nature" plays in our choices.
How much does this socialization really affect our choices? Does our evolutionary development play an equally powerful role in these choices? Bear in mind that we think that men were the hunters and women were the gatherers as we evolved into who we are today. This made a great deal of sense over the thousands of years of our existence. Since men were larger and stronger and possibly because their hormones made them more aggressive, they made better hunters. Women's hormones and greater endurance in tasks involving less physical strength made them better suited to gathering, food preparation, and all other tasks on the home front. Additionally, speaking of hormones, the "love" hormone, oxytocin, is generated in females as they bear children and breastfeed, promoting a bonding with their children that I do not believe is present in males, making them the most logical candidates to take care of the children. This hormone is likely to also promote a sort of "nest-building" instinct, which reinforces the notion of the woman as the homemaker.
Only time will tell how powerful our natures are vis-a-vis how we are raised. Much of our evolutionary makeup, of great use in times past, is not necessarily of much use today, in a cubicle, for example, where there is no need to be the largest or strongest. But it is hard to overcome things like hormonal impulses or the lack thereof. Will we evolve further in ways that reflect the needs of the times? What will be needed to survive and pass on one's genes?
Along with children’s observations of their parents, how a family raises their children also reinforces traditional or nontraditional gender roles. This includes characteristics such as how parents encourage or discourage certain types of play, certain types of dress, or certain kinds of interactions with siblings based on gender. If we look at the example of how parents encourage or discourage different types of play for boys and girls, we can see how they reinforce gender roles.
In families with traditional gender roles, parents and other family members may buy girls dolls and boys toy cars. They might discourage girls from playing in the dirt, but allow or even encourage boys to. This will reinforce the message for children that they should follow traditional gender roles, or may even lead them to believe that these roles are “natural” since they have been conditioned to follow them since they were infants.
On the other hand, if the family follows nontraditional gender roles, then they may try to buy both dolls and toy cars for both boys and girls, or they may even buy only what is considered nontraditional for a gender; for example, only buying dolls for a boy. This may teach their children that it is okay to have interests or behaviors outside of traditional gender roles; the children may not consider anything to be “just for boys” or “just for girls,” or they may think that not following traditional roles is something positive.
Of course, as mentioned above, sometimes children rebel against the way their families raised them, and may act the opposite of how their parents encouraged them to act or think, especially as they become adolescents and adults. So for example, a woman raised in a family that encouraged traditional gender roles and never let her play with toy cars might feel that that was an unpleasant experience and may decide to become a car mechanic. In this respect, acceptance of nontraditional gender roles can be encouraged by trying to impose traditional gender roles on a child and vice versa.