The Giver was not banned for one particular reason, but the most common objections to it were its depictions of sexuality, encouragement of defiance, and representations of euthanasia.
Most people would probably agree that The Giver is most appropriate for preteens and adolescents or teenagers who are mature enough to understand its adult themes. The presence of Stirrings, or sexual feelings, and issues of repressed emotion are not appropriate for every child.
For example, in one part Jonas has a dream about a girl his age in a bathtub. Although there is nothing sexual explicit, his parents recognize the dream as the first whispers of sexual desire and give him pills for Stirrings. The pills are designed to prevent people from having sex and producing children (or feelings of love).
Most objections to the book likely come from these things, but there are some that disagreed with the book’s depictions of euthanasia, including the murder of an infant. The scene is designed to shock, and is actually someone graphic in its own way.
As he continued to watch, the newchild, no longer crying, moved his arms and legs in a jerking motion. Then he went limp. He head fell to the side, his eyes half open. Then he was still. (ch 19, p. 150)
A child reading this scene without any guidance could be very disturbed. It is designed to shock and make one thing, and there should be conversations after reading it.
Some adults would disagree with the entire dystopia premise, arguing that it glamorizes parental and societal disobedience.
As with most books, this one should not be given to just any child. Some children will be disturbed and confused by this book. This is why it is so popular with teachers! In a carefully crafted lesson, this book is very powerful in opening young minds to the realities of a harsh world and the importance of individuality and choice.
Lowry, Lois (1993-04-26). The Giver (Newbery Medal Book). Houghton Mifflin Harcourt. Kindle Edition.