Mammograms are currently coming under a lot of scrutiny in the last few years since the U.S. Preventive Services Task Force came out with it's guidelines in 2009. Based on their interpretation of scientific data so far, mammogram screening should begin at age 50, with every other year follow up in 'normal risk' women. There has been much contentious debate on both sides between physicians of many different specialties, and it has even become a political football between Democrats and Republicans! Regardless, many physicians have reticence to change their practice because of the medical-legal environment in this country.
I think that every woman should be properly informed about any surgical procedure and how to best prepare for it, including the possible utilization of mammograms. I work with my prospective patient and her primary care physician to best imform her of risks, benefits, and alternatives to mammograms prior to a procedure. In general, however, my policy is no mammogram is necessary in low breast cancer risk, premenopausal women less than 45 years of age. This is especially true if she has very large and dense (non fatty) breasts. An alternative for women who have a family history that is significant for breast cancer, but are younger, or have dense breasts is MRI.
Once you have been properly informed, you have a right to have a mammogram if you want or refuse. Your refusal may mean going to another doctor though.
Best of luck!