Because The Beatles' "Butcher cover" was so controversial--not any less today than "yesterday" [(:]--there have been a range of speculations as to what The Beatles were up to when they pushed publishing the photo.
I was watching the 1966 French movie Masculin, Feminin and one idea suggests itself: that the cover was about an abortion.
In the movie one of the main characters, Madeleine becomes pregnant by another main character, Paul. At the end of the film, it's hinted that Paul committed suicide. When the police investigator asks Madeleine what she will do about her pregnancy, Madeleine says, "I don't know. I'm not sure. Elizabeth [her friend] suggested using a curtain rod." In a video discussion of the film with two French film scholars, one of them talks about how upsetting it was for a girl to become pregnant out of wedlock in the 1960's and how he had lived next to a doctor who performed illegal abortions.
I flatly think the film was about Paul McCartney (more on that later.) It's very possible that Paul got a French girl pregnant, wanted her to have the child, and that she chose to have an illegal abortion from a doctor. Because it was Paul who argued to have the photo widely published-- [see my May 29, 2010 post]--it was more than likely his protest.