Harris's answer is that people's personalities are not simply the result of genes combined with household environment. It turns out that children's peers have far more to do with the personalties they eventually develop than their parents do. If she's right, that is simultaneously relieving--and disconcerting--for parents. It is relieving because it means parents should not worry as much as they do to make sure the home environment is perfect. On the other hand, it is disconcerting because it means that much of the responsibility for how children turn out is outside the parents' control. Once the parents have contributed their genes, for the most part they are cut out of the picture.
There is more to the story, and Harris's full book is well worth reading. But here, to whet your appetite, is a selection of passages from the book:
1. "Differential treatment by parents--the tendency of parents to treat their children differently--accounted for only 2 percent of the total variance [in children's personalities]. Differential sibling interaction also accounted for 2 percent. Family constellation variables such as birth order and age differences between children accounted for only 1 percent" (p. 86).
2. "[...] the results showed sizable differences between siblings that could not be attributed either to genes or to aspects of the home environment they shared" (p. 86).
3. "[...] the results showed that parents were reacting to the genetic differences between their children, rather than causing their children to be different" (p. 87; italics in the original).
4. "Only highly abnormal conditions--conditions of severe deprivation--cause permanent deficits [in brain development]. The environment needs only to provide the bare minimum; beyond that minimum, there is no evidence that variations in quality or quantity make a difference" (p. 127).
5. "[...] interventions designed to improve parents' child-rearing methods might change children's behavior at home but will not affect their behavior at school" (p. 131). [I am not sure whether that makes me, as a parent, feel better or worse.]
6. "Because children discriminate sharply between situations, the way to improve their behavior in school is not by modifying their parents' behavior but by modifying their environment at school" (p. 135).
7. "[...] the assumptions that underlie popular theories of personality development--that learned behaviors transfer readily from one situation to another, that children learn things at home which they automatically carry with them to other settings, that their experiences with their parents will color their subsequent interactions with other social partners--are incorrect" (p. 140; italics mine). [The last, italicized part of that passage I found particularly striking.]