The reason that no one can explain to her that this idea is crazy is that we're probably dealing with her reaction to some deep trauma that she can barely remember. It's clear to me that there must have been some almost-forgotten incident in her past wherein she was deeply traumatized. Given that opinions and habits that are formed by extreme stress are nearly impossible to eradicate, those around her who believed that she would one day see sweet reason and admit that she'd misinterpreted what had actually happened to her and apologize to the people she falsely accused of doing whatever it was did so in vain. Whatever happened to her simply carved too deep a hole in her psyche to let facts fill the gap.
Also, by refusing to acknowledge her feelings just because she might have gotten her facts wrong, they helped to feed in to the belief that people just hate to hear her talk and simply want her to agree to whatever they say no matter what she might know or believe. We thus end up with a sort of vicious circle in which Elly's paranoid dread that she's expected to never talk or express herself worsens and causes her to ignore everyone else's feelings and expect her children to agree with everything she says. This is why she took an instant dislike to Michael the second he started talking in complex sentences and developed the need to pulverize him; after all, expressing his own opinion clearly meant that he didn't want her to express her own and that could not stand. One might as well tell her that she isn't hideous when she 'knows' better. More on that tomorrow.