What The Dickens?

There are programmes on the television that point out errors in famous films and from that point on you always notice them and wonder why you never saw them before. I have watched Charles Dickens 'A Christmas Carol' so many times each Christmas but it was only this weekend that i noticed a massive faux pas which i wish i never.
I always assumed the reason Scrooges father despised him and didn't want him at home was because his wife had died while giving birth to Ebeneezer the same as his beloved sister Fan died in childbirth to her son, Fred, helping to explain why Ebenezer so despised his nephew.
The Ghost of Christmas past even says when talking about Fan that: 'She died giving him life as your mother died giving you life'.
That always made sense to me, Scrooges mother died giving him life and his father blamed him and his sister died the same way and he blamed the nephew and as his father never allowed him to come home for Christmas holidays, he hated Christmas and thought it all 'humbug' but at the end of the film, when he turns up for Christmas dinner and dances the Polka, he comes to the realisation that he was blaming Fred for Fan’s death the same way Ebenezer’s father blamed him for his own mother’s death.
But...Fan was Scrooges younger sister, Dickens himself said when Fan came to collect him from the boarding school: 'a little girl, much younger than the boy, came darting in, and putting her arms about his neck, and often kissing him, addressed him as her 'Dear, dear brother.'
Oh dear, mother died giving birth to older brother which is the background to everything that happens after but somehow manages to have another child and call her Fan.
I'll put it down to Dickens being distracted by being called away to drag a child out the chimney or something midway through writing that scene and try to ignore it.