The anti-alcohol movement didn't invent junk science, but instead follows in some very well-trodden footsteps. Some of the most fertile ground for junk science is the indirect association -- a situation where two things seem related, but where, in reality, one does not cause the other.
However, if one does the intellectual gymnastics to believe that causation exists in an indirect association, then it is entirely possible to "prove" a great many scientific impossibilities.
In this context, it is possible to "prove scientifically" that education makes women infertile. The "science" goes like this: The birth rate among educated women is lower than uneducated women, therefore educated women are less fertile. This illustrates how junk science can look scientifically valid. But in this case, looking more deeply into other factors, you find that educated women are more likely to postpone (or forego) childbearing than uneducated women are. Thus, while lower birth rates are indirectly associated with education, education does not "cause" lower fertility.
This same sort of indirect association may account for the links between breast cancer and alcohol. However, since any link serves the political agenda of the anti-alcohol groups, they prefer to promote the studies and embellish the data that support their positions and cover-up the data that does not support their agenda.
Indirect associations are fairly common in nature which is why it is so important to take further steps -- to establish a mechanism of how the effect could happen, and to conduct animal studies that could confirm the association.
In this context it is important to note that while anti-alcohol groups promote junk science that "proves" alcohol causes cancer, no biological mechanism has been established for the action and none of the animal studies have shown it to cause cancer.