In one sense, My Abandonment is about a little girl's journey from kidnapping victim to kidnapping perpetrator. The interesting part of that interpretation is that the narrator doesn't explicitly say anything about kidnapping; instead, the novelist describes the day when Caroline's "real father" came to "save her" from her "fake family." Those are all in quotes, because Caroline never figures out whether he was telling the truth. Perhaps Caroline's father kidnapped her from her mother and stepfather, but otherwise, Caroline was abducted and is suffering Stockholm syndrome-like affection for her kidnapper.
When Caroline begins to scope out Portland for a little girl to abduct, she describes that urge in morally acceptable terms. She's not kidnapping anyone, she's just looking for a young girl who looks like they might want to escape their normal life. But, that's kidnapping. So, this story is at least in part, a demonstration of how children inherit the abusive tendencies of those who abuse them.
In another sense, the novel is a metaphorical exploration of a teenager's first experience with existential dread. As a child, things tend to make sense, but this novel shows Caroline's journey through her first time not getting what she wants. Taken from her wilderness paradise, Caroline ends up in a frozen tundra, nearly frostbitten to death, without her father beside her, alone, and from that paralyzing position, she decides the right thing for her is to get her degree and find a job. One might say that in that regard, Caroline succeeded in the major moral quest of the novel. But in the end, there's still a big question mark over Caroline's mental health.