Screening mammograms every 2 or 3 years, or even yearly, are no guarantee that breast cancer will be detected. After my GP ruled out breast cancer when I displayed what I later learned was a symptom ("nothing to be concerned about"), my breast cancer (Lobular) was not discovered until a year later, when I was finally sent for a diagnostic and ultrasound. Diagnosis: stage 3 (T7 N14 M0). 
The cancer had been there for at least 3 - 5 years when it was discovered, and I had been having yearly screening mammograms throughout that time. Educating women about the symptoms of breast cancer rather than relying solely on screening mammograms is essential, as is a healthy disrespect for GPs when the patient senses that something is not right.  I learned the hard way.