Estrogen-Induced Proliferation of Existing Mutant Cells
Although estrogen does not appear to directly cause the DNA mutations that trigger the development of human cancer, estrogen does stimulate cell proliferation.
Therefore, if breast cells already possess a DNA mutation that increases the risk of developing cancer, these cells will proliferate (along with normal breast cells) in response to estrogen stimulation. The result will be an increase in the total number of mutant cells, any of which might thereafter acquire the additional mutations that lead to uncontrolled proliferation and the onset of cancer.
In other words, estrogen-induced cell production leads to an increase in the total number of mutant cells that exist. These cells are at increased risk of becoming cancerous, so the chances that cancer may actually develop are increased.