Bagels and choo me too.
I once asked a psychotherapist the same question. Her reply was that healing is always possible. This shows that while a => b, b doesn't necessarily imply a.
Going back 3 generations of my family, there's been a female paedophile, ready to toe the family line, get the inheritance etc and a rebel. In my grandmother's generation there was also a 'spare'.
My aunt and godmother deliberately didn't have children she was so worried about the outside chance she'd be like her mother, who when she was pregnant starved herself to such an extent that when my aunt's teeth came through they were black. Her reply when my poor aunt said that she couldn't smile because of her black teeth? To keep her mouth closed. She was admitted to a sanitorium in the 30s, not because of TB as my late mother told me, but because she had been so malnourished.
My grandfather was a pharmacist, and wasn't even allowed to sleep in a bed after they were married, just a single bed. Their first child was born 3 years after marriage. Don't know if there were threats of annulment due to non-consummation, but obviously Grandpa was given rights of access 3 times. I had her bedroom furniture, a single bed. She died just after I was conceived, my mother lost weight down to less than 7 stone, apparently - according to a friend - didn't know she was pregnant and thought it was the menopause. I now have quite a lot of health problems - born 2 months early and my mother let me lose over a pound in weight before anything was done in the nursing home.
The problem is that with no-one to turn to, the children victimised have to be extremely strong not only to not develop the personality of a victim, but to not toe the party line. Then what happens is that the abuse is normalised and internalised, and continues to the next generation. Thankfully I was an only child, which helped me. Had there been a second, I was told, they would have probably been the Golden Child, and I would have been even more 'shit of the universe'.
My aunt said that her mother hated her. It was true. I can remembering trying it on for size, and it explained perfectly the way she behaved towards me, too. As her mother did to her father, she made my late father's life hell. My uncle is very bitter about the way she was treated by her family, but, thankfully doesn't seem to bear me any grudge. Time will tell. He thinks I had a happy childhood, but wasn't around to see. Not terribly comfortable for him to admit the truth.