For starters, false positives are an inherent part of medical diagnosis. Interpretation and diagnosis is probabilistic based on ROC curves balancing different sensitivities and specificities balanced with disease prevalence as well as the significance of missed/delayed diagnosis.
Every concern that has been raised in these comments is factored into our reporting system. All radiologists use the BI-RADS reporting system which is internationally validated and expresses probabilities of malignancy to guide further management based on specific imaging. features that have been validated against pathologic data from excised surgical specimens and biopsies. This was done to homogenize reporting practices.
For example a BI-RADS 5 lesion, which is based on specific imaging features not a gestalt/expert opinion, denotes a 95% probability of malignancy and would generally result urgent biopsy + surgical consultation. A BI-RADS 3 lesion has a 2% chance of malignancy and would generally be followed with serial imaging for a specified interval.
BI-RADS 4 is the middle, this is broken down into A/B/C but essentially anything with 3%+ probability goes for biopsy. That means we expect up to 97% of the lesions we biopsy will have been false positives.
This is intentional and desired, this is because the harms of missing breast cancer is horrible, early detection results in treatment with lumpectomy + radiation vs advanced breast cancer needing systemic therapies and radical resections.
Second, what happens when there is an abnormality on a screening mammogram is not straight to biopsy. We use additional mammography views and ultrasound to help us find out what's going on before making that decision. We also have MRI to troubleshoot and increasingly for screening, certainly for high risk and extremely dense breasts.
Tomosynthesis or 3D mammography is not a cure-all for false positives, it's also not intended for dense breasts. The point of Tomosynthesis is to reduce callbacks for overlapping breast tissue which can sometimes look like a real cancer, and to increase sensitivity for architectural distortion (an occult or infiltrative cancer distorting the fibroglandular architecture) which can be really hard to pick up on 2D.
It works really great for that. Patients with extremely dense breasts should really be getting screening MRIs (US as a lesser alternative) in today's age and this is happening with increasing frequently.
Further reading:
https://en.wikipedia.org/wiki/Receiver_operating_characteris...
https://www.acr.org/Clinical-Resources/Reporting-and-Data-Sy...
https://www.nejm.org/doi/full/10.1056/NEJMoa1903986
https://www.cancer.gov/about-cancer/treatment/clinical-trial...