Why did the Giver show the release to Jonas?

The Giver has been gradually giving Jonas all of his memories, and he has taken note of how Jonas has responded, with his questioning and his critical response to the ways and rules of the community.  And as old and tired and nearly hopeless as he seems to be, he sees something in Jonas that makes him believe there could be a change.  So the Giver shows Jonas the release of the infant in the hope that Jonas, being shown the full horror of the community's ways, will help effect a change. 

What the Giver has been hoping for becomes clear after Jonas sees the release.  Jonas is distraught and in complete rebellion against the idea now that he understands what release is—people are being deliberately put to death, underweight infants, the unproductive elderly, stray pilots, and probably others who have disobeyed the rules. This understanding is the final straw. The ordinarily obedient Jonas refuses to return to his parents. He understands that people have given up feelings, color, sunshine, sexual desire, and now, even their lives to ensure safety and prosperity. His father is a murderer, and everyone is compliant in the release process.  

The Giver arranges for Jonas to stay with him and not return home. They talk and eat, until Jonas calms down a bit. The Giver explains that he has learned from Jonas, too, and he says,

...having you here with me over the past year has made me realize that things must change. For years I've felt that they should, but it seemed so hopeless (154-55).

The Giver has come to the conclusion that sending Jonas off with some of the memories will enable him to function Elsewhere and perhaps be able to save the community from itself, its dreadful sameness, security, and unfeelingness.  He understood that sharing the release with Jonas would be the means of horrifying Jonas enough to be motivated to leave.  To some degree, it's fair to say that he manipulates Jonas, but for the greater good of Jonas and the community. 

The entire book is directed to this moment, when Jonas' intelligence and now his knowledge make the Giver understand that he is the hope of the community.  If the Giver had simply transmitted memories without showing Jonas this final horror, Jonas would probably have become the Giver, and things would have gone on as before.  It is the Giver's manipulation that allows this dystopian novel to end on a note of hope.