The point of screening is you can decide what to do if anything is found. It's not an automatic conveyer belt of treatment. I have private treatment and know that at any time i can stop and think about what I'd want next.
The problem is that it does become an automatic conveyed belt of treatment. If an abnormality is found, you will be strongly pressured to go ahead with treatment, and you will say yes, and who would blame you. It is hard for a patient to "wait and see" and impossible for a doctor to recommend, because of fear you might sue them.
Breast cancer and prostate cancer screenings often lead to people being maimed (breasts removed, prostate removed = impotence, incontinence), suffering pain from surgery and chemotherapy and some have died from complications during surgery - possibly they had an abnormality that would never have harmed them. Yes you might be one of the ones who's cancer is found early, but statistically you are more likely to be the one that has chemotherapy for no reason.
And for the pp that commented that a mammogram has less radiation than sitting in front of the tv! Not true, radiation used in mammography is x ray, which is ionising radiation.
It's these types of misunderstandings that screening advocates do nothing to correct and even encourage because "it gets women in the door". Well I don't think people need to be tricked. I am not against screening, but I think it should be each person's own decision based on their own personal risk profile.