I actually think it has little to do with that.
I look at the main reasons people give now for having kids, mainly that its something THEY want, its an experience THEY want in their lives. Children, in spite of what you have heard, have a measurable deleterious effect on your happiness. Children are hard, children are difficult and if we are all Self-Actualized adults pursuing our self interest and our own happiness, children are an odd thing to personally do.
Because the center of ones life is themselves and not family, the clan or the tribe, people focus exclusively on ones own pet pleasures, and thus forgo children. Basically sterility is a disease of modernity IMHO.
Women working is a red haring, plenty of non-feminist cultures have low birth rates, indeed much of the world does and soon the whole world will.