Why does Dave's mother choose to abuse him only and not the siblings in A Child Called It?

This is a question that the reader must struggle with throughout the book, just as David wrestles with the same conflicted idea. His abuse at the hands of his mother was horrific; she made him swallow vomit, feces, and ammonia. David survived being choked, stabbed, and almost starved by the woman who was supposed to love him most in the world.
Even as an adult, Pelzer does not know with certainty why his mother singled him out for abuse. He says that his mother claimed she was abused by her own mother (which his grandmother denies). He questions whether she was completely overwhelmed in being a single mother to five young boys. And he thinks that maybe she suffered from an undiagnosed mental illness. Regardless of the root source of her dysfunction, her alcoholic tendencies likely made the situation incredibly worse. In fact, her boys donated her body to science when she died, and her liver is now displayed at the University of Utah's medical center as an example of a "grossly diseased organ."
A cousin of the family describes Dave's mother as "a mess, a total recluse." Her own mother said that her "daughter told me I was not a member of the family. Alcoholism does strange things to people."
In cases of horrific abuse, it is natural to look for a reason that could cause one person to turn so unjustly and horrifically on another. However, in the brains of those who seek to abuse children, there simply is no logical reason for such cruel behavior, and it is impossible to ever understand why David's mother treated him with such violent contempt while sparing his brothers.
In short, she was a very sick woman.
http://archive.boston.com/news/globe/living/articles/2006/04/26/family_feud/

In A Child Called It, the narrator, David, shares stories of abuse by his mother. David's mother suffers from depression and is an alcoholic. She refers to her son as "It" and punishes him by withholding food, beating him, and forcing him to swallow ammonia. David learns that his mother's physical appearance often allows him to predict how he will be treated. If she spends time on her appearance, she will often not treat David as harshly.
David does not state exactly why his mother targets him and not his brothers. David's brothers are treated as part of the family, while he is excluded. In the first chapter of the book, as David is in the room with the police officer and school staff members, he tells them, "Mother punishes me because I am bad." In his second book, The Lost Boy, David recalls thinking his mother was sick and that perhaps that could be the reason why his mother only targeted him.

A Child Called It, written by David Pelzer, tells of the horrible abuse one child faced at the hands of his mother. Although David, the first-person narrator, never openly states why his mother chose to abuse him over his brothers. Yet one can infer about a few reasons David's mother abused him and not his brothers. First, David's voice "carried farther than others." It seems that his voice got on his mother's nerves. Second, David seemed to get "caught at mischief" more than his brothers. His numerous mischievous moments angered his mother greatly. Third, David's mother is an alcoholic. Given David's voice and "mischief," her drunkenness during these moments would force her to lash out at David, as well.
David's mother came to call him a "bad boy." Because she identifies him, over his brothers, as the bad child, her anger is always directed at him. David's mother also believes her husband, David's father, cares too much for him. When he is away, David's mother treats him (David) very poorly to discipline him for his father's loves.
Although not a reason named in the text specifically, David's mother could have some type of mental illness (which she self-medicates with alcohol). One could argue that she suffers from postpartum depression (a depression which follows the birth of a child). The PPD could have come on after David's birth, and she could blame him for her falling into depression.