Question

In the Torah, in the section on valuations, the monetary valuation of a woman is lower than that of a man of the same age. I admit and confess that I haven’t studied the topic in depth, and I really don’t know exactly what the obligation of valuations means. Even so, this fact really troubles me. If valuations are literally some kind of assessment of the “value of a person’s life,” it comes out that a woman’s life is worth less than a man’s life.
Rashi on the Torah there says something a bit different: “And if from sixty years old and upward, etc. — when one reaches old age, a woman comes closer to being considered like a man; therefore a man’s valuation is reduced in his old age by more than a third, while a woman’s is reduced only by a third (Arakhin 19), for people say: an old man in the house is a burden in the house; an old woman in the house is a treasure in the house, and a good sign in the house.” If I understood correctly, Rashi’s point is about people’s roles: for example, a young man who goes out to work has more value than a woman who stays home and raises children, but an old grandfather who sits in an armchair all day is less useful compared to a grandmother who keeps doing the housework. And from our present-day perspective, that explanation seems even more puzzling to me — did the Torah set an eternal value based on the gender roles that existed in the ancient world?
It seems to me that valuations are supposed to have some underlying logic that ought to be intuitive to us. After all, a person aged 20–60 is worth more than an old person or a child, and at least intuitively that is clear. And it seems to me that the gap there between men and women is supposed to work according to that same underlying logic, which was presumably intuitive to people in the ancient world. But if so, it simply comes out that the eternal Torah contains a very chauvinistic principle. How can that be?