Why is precision of language so important to the people of Jonas's society?
Language "precision," as it is called, is another tool used by the society of The Giver to control the community and keep them content and safe by desensitizing them.
In his essay "Politics and the English Language," George Orwell writes,
Now, it is clear that the decline of a language must ultimately have political and economic causes....(http://www.orwell.ru/library/essays/politics/english/e_polit/)
In this passage and further in the essay, Orwell writes of the power of language. Certainly, language is is a tool for powerful governments; indeed, it is a type of thought control. Continuing some of Orwell's ideas from this essay, he writes, "If thought corrupts language, language can also corrupt thought." This is the very concept behind the invention of Newspeak in Orwell's 1984.
Similarly, in the society of The Giver, language is used to control and corrupt thought. In order to control any intense emotion, which could cause negative results, the society has people discuss their feelings, but only with "precision"; that is, they are restricted to approved words that can be used in the community. Many of them are mere euphemisms, words which are rather innocuous and will neither stir deep emotion in the speaker nor excite it in the listener. By requiring people to use these euphemisms, the thoughts and emotions of the citizenry can better be controlled, as well as modified.
In Chapter 1, for instance, as he rides his bicycle home, Jonas worries over his word choice for the evening ritual in which the members of his family share their feelings about the events of the day. Later, after one of Jonas's family expresses feelings, the others commiserate and offer their words of comfort or support. But, these words really are all too sanguine to be genuine or comforting. In fact, Jonas finds that he must "sift through his complicated emotions" to find the soft words demanded by his society. When he does this, he is left unsatisfied. For instance, as Jonas nears home, he contemplates the upcoming Ceremony of Twelve in which he will receive his Assignment for his life:
...he realized that frightened was the wrong word to capture his feelings about the momentous ceremony.....It was too strong an adjective.
Even though he is eager, excited, and rather nervous about the ceremony, Jonas knows that he must not express all these feelings. So, instead, he decides upon the more euphemistic adjective apprehensive and uses it to describe his feelings about the forthcoming December ceremony. His father merely tells him, "I'm glad that you told us of your feelings."
This sedated conversation of the family keeps a certain calmness in the home, but it also makes for a desensitized and empty life. Nevertheless, this desensitized life is desired by the community because it is safer for the members of the society as they are less likely to disobey the rules or conflict with one another or the authorities than if they expressed powerfully their emotions.
The society of Lowry's novel is created by those who want to eliminate all the conflicts, pain, and griefs to the safe keeping of one person, who alone bares the burdens of these human agonies and emotions. While this one person, who is called the Giver, carries memories and bears the burden of pain and deep emotion, the others opt for sameness over individuality and safety over freedom. And, language is one tool used to maintain this structure.