Mammography screening has been promoted to the public with a simple promise It saves lives and breasts by catching the cancers early.
Screening does not seem to make the women live longer; it increases mastectomies; and cancers are not caught early, they are caught very late. There is so much overdiagnosis that the best thing a women can do to lower her risk of becoming a breast cancer patient is to avoid going to screening, which will lower her risk by one-third 
A Study from the Journal of the Royal Society of Medicine Concludes -
"I believe that if screening had been a drug, it would have been withdrawn from the market long ago. Many drugs are withdrawn although they benefit many patients, when serious harms are reported in rather few patients. The situation with mammography screening is the opposite: Very few, if any, will benefit, whereas many will be harmed. I therefore believe it is appropriate that a nationally appointed body in Switzerland has now recommended that mammography screening should be stopped because it is harmful." Nordic Cochran Centre - More recent studies suggest that mammography screening may no longer be effective in reducing the risk of dying from breast cancer. Screening produces patients with breast cancer from among healthy women who would never have developed symptoms of breast cancer. Treatment of these healthy women increases their risk of dying, e.g. from heart disease and cancer.
It therefore no longer seems beneficial to attend for breast cancer screening. In fact, by avoiding going to screening, a woman will lower her risk of getting a breast cancer diagnosis. However, despite this, some women might still wish to go to screening.
Mammograms are unreliable - Normal breast tissue can hide a tumour so that it doesn't show up on the mammogram. This is called a false negative. And mammography can identify an abnormality that looks like a cancer, but turns out to be normal, false positive
Nordic Cochran Centre, the US and the Canadian Task Forces, the Independent UK Panel and the Swiss Medical Board have found substantial problems with the randomised trials.1–5 It is therefore difficult to know what the true effect is.A study that compared three pairs of very similar neighbouring countries that had introduced screening 10–15 years apart16 found no relation at all between start of screening and the reduction in breast cancer. Breast cancer mortality is the wrong outcome. Not only because it is biased in favour of screening but also because the treatment of overdiagnosed, healthy women increases their risk of dying. Radiotherapy, for example, may cause deaths from heart disease, lung cancer and other cancers, and these iatrogenic deaths are not counted as breast cancer deaths. 
Radiation - On average, annual screening of 100,000 women aged 40 to 74 years was projected to induce 125 breast cancers (95% confidence interval [CI]=88–178) leading to 16 deaths (95% CI=11–23) relative to 968 breast cancer deaths averted by early detection from screening. Women exposed at the 95th percentile were projected to develop 246 radiation-induced breast cancers leading to 32 deaths per 100,000 women. Women with large breasts requiring extra views for complete breast examination (8% of population) were projected to have higher radiation-induced breast cancer incidence and mortality (266 cancers, 35 deaths per 100,000 women), compared to women with small or average breasts (113 cancers, 15 deaths per 100,000 women.
Rupture tumours - Mammography involves compressing the breasts between two plates in order to spread out the breast tissue for imaging. Today’s mammogram equipment applies 42 pounds of pressure to the breasts. Not surprisingly, this can cause significant pain. However, there is also a serious health risk associated with the compression applied to the breasts. Only 22 pounds of pressure is needed to rupture the encapsulation of a cancerous tumor . The amount of pressure involved in a mammography procedure therefore has the potential to rupture existing tumours and spread malignant cells into the bloodstream ,
 - https://pubmed.ncbi.nlm.nih.gov/19589821/
 - https://www.cochrane.dk/screening-breast-cancer-mammography
 - https://www.nejm.org/doi/full/10.1056/NEJMp1401875#t=article