Sex steroid hormone levels are strongly related to breast cancer development, and a diet high in fiber has been hypothesized to reduce breast cancer incidence by inhibiting reabsorption of estrogen, thus decreasing circulating levels.
You may want to refer to the paper attached below for more information.
Previous studies of fiber intake and breast cancer have almost all been non-significant. This particular study examined diet during adolescence or early adulthood, a period when breast cancer risk factors appear to be particularly important.
Article Dietary Fiber Intake in Young Adults and Breast Cancer Risk
The findings in this study support the hypothesis that consumption of foods high in fiber reduce breast cancer risk. The results also suggest that dietary fiber intake (foods rich in fiber such as fruits, vegetables, and whole grains) during adolescence and early adulthood may be particularly important.