I haven't been in a violent relationship, but I've read a fair amount on why people frequently don't leave.
One piece is that physical abuse is commonly accompanied by emotional abuse-- the abuser keeps saying that the abusee is to incompetent to live on their own and too unattractive to get another mate. It's not uncommon for people who feel they are in an inferior position, whether because of violence or just because the other person sounds very certain, to accept that sort of assessment.
There are women who stay because the man is the best father they think they can find, and leave when they realize he's abusing their children.
I'm being gender-non-specific for most of this because, while men are apt to have more financial resources to leave and perhaps less reason to fear extreme violence, the emotional dynamics aren't too different.
Sometimes the abuse has built up slowly. People can be very bad at judging how bad a situation has become, especially if the problems are intermittent.
Sometimes the abuser is inconsistent-- alternating abuse with intense apologies and/or affection. This can make the abusee confused, especially if they've bought into the idea that "love" excuses everything. Not just the abuser's claims of loving them, but that they feel love for the abuser means that the abusee shouldn't care about their own quality of life. This isn't just personal pathology, it's part of the culture.
Also, abusers are apt to isolate their victims from friends and family, thus making practical and emotional help with leaving less likely.
While it's fading, it's not uncommon to believe (sometimes for religious reasons) that family stability should completely trump personal quality of life.
It's financially difficult to leave.
Abusers are apt to become more violent (sometimes to the point of murder) when they feel abandoned.
Thanks, that's a helpful summary. (And, regarding the topic, I don't that explanation requires one to have been abused to understand.)
Sometimes in an argument, an older opponent might claim that perhaps as I grow older, my opinions will change, or that I'll come around on the topic. Implicit in this claim is the assumption that age or quantity of experience is a proxy for legitimate authority. In and of itself, such "life experience" is necessary for an informed rational worldview, but it is not sufficient.
The claim that more "life experience" will completely reverse an opinion indicates that the person making such a claim believes that opinions from others are based primarily on accumulating anecdotes, perhaps derived from extensive availability bias. It actually is a pretty decent assumption that other people aren't Bayesian, because for the most part, they aren't. Many can confirm this, including Haidt, Kahneman, and Tversky.
When an opponent appeals to more "life experience," it's a last resort, and it's a conversation halter. This tactic is used when an opponent is cornered. The claim is nearly an outright acknowledgment of moving to exit the realm of rational debate. Why stick to rational discourse when you can shift to trading anecdotes? It levels the playing field, because anecdotes, while Bayesian evidence, are easily abused, especially for complex moral, social, and political claims. As rhetoric, this is frustratingly effective, but it's logically rude.
Although it might be rude and rhetorically weak, it would be authoritatively appropriate for a Bayesian to be condescending to a non-Bayesian in an argument. Conversely, it can be downright maddening for a non-Bayesian to be condescending to a Bayesian, because the non-Bayesian lacks the epistemological authority to warrant such condescension. E.T. Jaynes wrote in Probability Theory about the arrogance of the uninformed, "The semiliterate on the next bar stool will tell you with absolute, arrogant assurance just how to solve the world's problems; while the scholar who has spent a lifetime studying their causes is not at all sure how to do this."