I'm one of those people who won't go, either.
I weighed up the pro's and cons, like never having been on 'the pill', not having any history of breast cancer in our family and also the chance that I could be one of those people who only get it because of having the mammogram in the first place.
My view is that if the odds are 1 in 12 people (as they say) then around 92 women are screened unneccesarily. Add to that the fact that I was once told (after ultrasonic tests) that I had fibroids, went into hospital for a D&C, to be told that I didn't have fibroids "just a small polyp which I have snipped out", only to be told later that I did have a fibroid as big as a four month pregnancy after all ... something which I still live with because it doesn't give me any problem and is probably shrinking nicely now that I'm past menopause.
I was also told that I had gallstones, again after ultrasonic testing, had to then go for a barium enema which discovered that I didn't, after all, have anything of the kind.
With a history of misdiagnoses, I'm reluctant to have a mammogram anyway due to the suspicion that they would say I had breast cancer, take my breast/s away only to discover that I hadn't when it was too late.
I seriously question routinely x-raying great numbers of people for anything they MIGHT have, ever since I sat down and thought about the fact that when I went to grammar school, I, and all the other children were bussed into Nottingham every six months for chest x-ays, and this went on for the whole five years attendance at a time when our little bodies were in the process of development. Also, there was a time when dentists x-rayed teeth regularly, a practice that they have since thought more about and do more to protect their dental nurses from too much exposure. So, I believe that my body has had more than its fair share of being irradiated without good reason.