And yes I know Eola's speech isn't necessarily true about the player character, as she's capable of making people think what she wants them to think like when she convinces Verulus to lie down on the altar by telling him he's tired. It was her way of manipulating the dragonborn into helping her coven. I was just saying there aren't many other moments when somebody mentions your past.
I always interpreted Eola's speech in the same way as Brynjolf's little "never earned an honest coin in your life, have you?" speech, myself. She looked at you and 'thought' she saw something of herself in you, and hoped that by just coming out and saying it, you'd be amenable to admitting as much. While Brynjolf incentivised admitting to it with the offer of steady coin for your nefarious deeds, Eola incentivised admitting to it with the idea of acceptance and comradery for something that is otherwise socially shunned. Both incentives would make it easier for someone to come out and admit to something, I think, hence why they did it. For example, it's probably much easier to admit to someone that you're an alcoholic or a drug user if the person asking admits to being one too, if that makes any sense.
I tend to dismiss the idea that she was trying to magically influence the player into having a false memory, as it's pretty easy to just dismiss her suggestion out-of-hand (and then kill her for suggesting it); yet later on she was able to compel that guy to lie down and
get eaten, which you'd think would have been even
easier to resist. And I don't think it was Bethesda trying to establish a past for your character either, as again, you can dismiss her suggestion out-of-hand. It's up to you if her guess was correct. My goody two-shoes characters have invariably reacted negatively to Brynjolf's suggestion that they are thieves, taking offence at the insuination, and they've obviously reacted even
worse to Eola's suggestion that they were cannibals. Just because they
think you're a thief or a cannibal, doesn't mean that you
are. Unless you are, in which case BONUS!!!, they just found themselves a friend!
It's a pretty risky game to play on their part, though. The way Brynjolf just wanders up to you at random and blurts out that he's a thieving scumbag and thinks you might be too is a bit of a dangerous thing to do, even in a place as corrupt as Riften. There's nothing stopping people from immediately running off to the guards and ratting him out, and even if that results in nothing, he could end up with a greatsword through the gut for his troubles (I know that in game-terms he can't, because he's essential, but I'm thinking practically). Eola's game is even
more dangerous, as she admits to being a cannibal to a heavily-armed stranger in the middle of a
completely empty Hall of the Dead, and given how reviled cannibalism is in most of Tamriel (besides Valenwood), any number of ill fates could befall her if she admits it to the wrong person... and often have, in fact!
As for why Bethesda decided to animate your cannibalistic acts, well... I suppose it just wouldn't have the same
"ewww.... what have I just done!" effect if you just stood there motionless and gained a health boost. It's cannibalism we're talking about here, it's
supposed to be gross.