Evidence does suggest that women who never had children are at a slightly elevated risk of breast cancer. To understand why this is the case, you need to understand the connection between estrogen and breast cancer.
Estrogen alone does not cause cancer. The hormone, estrogen, is an essential part of a woman's physiology. However, estrogenís principal function is to speed the process of cell proliferation. Therefore, estrogen can increase the chance of a mutation occurring and/or encourage the growth of cancerous cells once they appear.
The more estrogen a woman is exposed to during her lifetime, the greater the opportunity for the hormone to promote the growth of a tumor. During pregnancy, estrogen production decreases. Thus, women who have never been pregnant have had more exposure to estrogen during their lifetime, which puts them at a slightly higher risk for breast cancer.