Antiperspirants have aluminum-based compounds that act as plugs within the sweat glands that stop one from sweating excessively.
There are some research that skin may absorb the aluminum due to long term and frequent use of Antiperspirants and may have estrogen-like effects. Estrogen can promote the growth of cancer cells.
As of present date, however, there are still NO evident and confirmed substantial adverse effects of aluminum that could potentially put one person at risk of having breast cancer.
If you are still wary about your health and still afraid you might develop breast cancer, you may look for some Non-toxic Deodorants or Antiperspirants. Find some products that does not contain Parabens. Because Parabens can disrupt hormones and are linked to certain cancers.