An article here mentions a survey where women who wore bras were much more likely to get breast cancer. A google search on the subject will offer a lot of other cites, though many of them seem to have an axe to grind.
It would be very interesting to see if there was a correlation between wearing a bra and getting cancer. It could be why breast cancer seems to happen much more frequenly in developed countries, particularly the United States.
Well, I’m a guy and I don’t have breasts. My WAG is…I CERTAINLY HOPE SO! 
Sorry I don’t have the specific reference, but that “study” was done by a man & wife on some remote island. Neither had a medical background. Since they didn’t encounter any women with breast cancer, & after questioning the populus, they surmised it was the lack of bras. They chose not to take into account the people ate mostly fruit & fish, no preservatives, didn’t drive cars, didn’t even have electricity. The Paper was so flawed, I don’t think any one else ever looked into it… Of course, I could be wrong.
If there is any correlation, it is likely to be that women with larger breasts are more likely to wear bras.
It may be that just being larger means they are more likely to get cancer there, or their breasts may undergo more traumas, which in turn can trigger cancers.
I sure hope you don’t think having undeveloped breasts makes you immune to cancer. A small number of men get breast cancer every year. Everything a women’s breast has is also present in a man’s - milk ducts etc. All you guys out there, if you happen to find a lump, don’t shrug it off, get it checked!
I seem to remember an article in Reader’s Digest that siad wearing a bra was linked to breast cancer, after a study was done in societies where women don’t wear bras v’s women who do … aupposedly there were more incidents of breast cancer in those who wore a bra for more than a few hours a day. I’ve since read elsewhere that the study was a bit bogus, and women shouldn’t pay any attention.
And BTW 1kBR Kid, for a woman with a bust over a C cup not wearing a bra is increadibly uncomfortable, even if it does get you a lot of attention 
I don’t know the validity of it, but I heard it was mostly linked to underwire bras. It may even be just poorly fitted underwire bras, too. But supposedly the wire exerts enough pressure to interfere with blood flow and such. Anyhow, I agree the study is probably mostly bogus, but it might be a good idea to make sure the bra is not interfering with circulation.
According to this article , obesity is linked with breast cancer. I’ve noticed that less endowed women (like my wife) tend to wear bra’s less often.
Did they control for gender?
I don’t know for sure as I have not reviewed the studies, but my guess is this is probably more related to age than wearing a bra. In other words, women in developed countries tend to wear bras more so than those in less developed countries and also tend to live longer. The older you live to be, the higher risk of breast cancer. Therefore, if you wear a bra you are more likely to be in the group to get cancer also. You could just as easily “conclude” that wearing a bra makes you more likely to live longer, but this statement would also be very misleading.
Whatever the reason, I don't buy it for one minute.