One of the complaints about annual mammograms is the possibility of false positive results. They can cause emotional trauma years later.
Any false positive test result can be very scary. I am very sympathetic to this. No one wants to be told they have something 'bad' and to be told that they have something 'bad' and then be told that they were wrong, would be worse. But from my point of view (with my medical history) I can say having something 'bad' is infinitely worse than not having something 'bad'.
To understand my point of view, look at my medical history.
In 1981, I was told I probably had a goiter on my thyroid or something but they needed to operate to be sure because this was the time before biopsies. A goiter could cause problems in the long run so they went to take it out. Surprise, surprise, not a goiter but a tumor, and a malignant one to boot into lymph nodes as well.
Then in 1984, I had a breast lump. As I was already in the class of 'with your medical history, we need to be sure' and it was before breast biopsies, I had to have it out. I was happy to be told it was not cancer but a benign tumor. But I did get to stress through it.
Repeat regularly through the next 20+ years of 'with your medical history, we need to be sure'. I have had uterine fibroids that were 'sliced and diced' (to use my surgeon's words) to check for cancer after removal. I had that nasty mammogram in 2007 which led to all sorts of medical adventures. Then after chemo I had another tumor - how did that happen? (I am probably the only person on record to grow a tumor during chemotheraphy.) But it was benign. After a great deal of stress on my part.
I would not want to have a false positive mammogram or any test at this point but isn't it better to test and have the occasional false positive than to have people not be diagnosed until too late?