The article says:
Many cancer groups opposed the decision, and it's easy to see why: their job is to ensure that no one, no matter how slim the odds, dies of cancer that could have been prevented. Proponents of evidence-based medicine say that mammograms lead to too many unnecessary tests and the detection of too many tumors that may not really need treatment. But as it turns out, mammograms themselves aren’t the problem.
I can understand the impulse to dismiss the harm of a false-positive, but everyone assumes that the mammogram isn't susceptible to false-negatives. Everyone brings up their friend who was the exception to a rule as evidence that the rule is useless, but weird stuff confounds even very accurate tests (which the mammogram is not). It took me a long time to recognize that I am a vanishingly rare exception, so my experience with medical misadventures isn't really relevant to basically anyone.
I think I have emotional standing to assert that exceptions aren't what we should base standard practices around, so I don't want to hear about your grandmother who caught her breast cancer early with a mammogram before the age of 50. It is pretty nice when people luck out and get useful information from a mammogram in their 40s, but most of the time, all you get from a mammogram is a confirmation of what you knew to begin with. Plus, a patient undergoing mammography is exposed to radiation, and that's best avoided.
On a barely-related and sort of silly note, I always think of how the children in A Series of Unfortunate Events were subjected to unnecessary surgery, which has caused me to associate unnecessary medical procedures with melodrama more strongly than I should. Plus, I should admit that I have probably had an unnecessary MRI or two over the past few years, but I'm not about to argue with my neurologist as he tries to feel his way around the unlit area where my health hangs in the balance. If anyone has a good chance as guessing right, it's him. My somewhat-educated feeling is that I'll probably be okay, and if I go four or five years like I have been, I'm probably out of the woods.