The difference between the role of mother and father, such as having a job and taking care of the children, is common in most societies. I believe that the reasons for these differences are historical moments and other stereotypes.
One of the top differences between mothers and fathers is working and taking care of a child. In most countries, especially in Central and Middle-East Asia, father is the only person who earns money, while mother babysits and does home responsibilities. The reason could be that men are physically stronger than women, so only men should have a job. However, in our generation, there are lots of jobs with no physical requirements, such as teaching, cooking and other computer work. I think, in the future, parents will both have a job and take care of their kid and home.
The second common difference is that mothers mostly like their daughters rather than sons, while fathers do vice versa. In most cases, the daughter helps her mother with cleaning the house and cooking. At the same time, son does more physical work like fixing lamps or car, helping his father. But in Europe countries, anyone can involve in anything, no matter what their gender. It might be caused by gender stereotypes founded historically. I think, the future parents won’t differ and differ their children by their gender.
In conclusion, parents’ difference are mostly related to steretypes and history.