Why does Jonas refuse to go home?
In Ch. 20 Jonas refuses to go home because he has just seen a video of the "release" that his father performed on a newborn twin that morning at the Nurturing Center.
Up until this point in the novel, Jonas has not really understood what "release" really meant. As a result, he has also not fully understood his father's role as a Nurturer. Once he does see what his father did during the "release", lethally injecting a perfectly healthy newborn baby and then discarding his body into what appears to be a trash chute, Jonas is horrified and traumatized. He also feels betrayed by his father and his community that has sanctioned this behavior.
"But he lied to me!" Jonas wept.
"It's what he was told to do, and he knows nothing else."
"What about you? Do you lie to me, too?" Jonas almost spat the question at the Giver.
Jonas is trying to come to terms with how someone he trusted so completely, his father, could commit such a heinous act. He is so shaken, he no longer knows who to trust or what to believe, so his anger and distrust come out at the Giver, at first.
Jonas stays with the Giver that night because he is too distraught to go home after all he has learned. He literally would not know what to do or say around his father.
In Chapter 19, the Giver allows Jonas to watch a release ceremony in order to discover the dark truth behind the community event. Jonas then watches as his father kills an infant twin via lethal injection and simply disposes of it into some sort of trash chute. Jonas is shocked and horrified after discovering the dark truth behind the release ceremony and refuses to go home at the beginning of Chapter 20. Jonas begs the Giver not to make him go home that night because he is so disturbed after watching his father kill the innocent baby. The Giver then explains to Jonas that his father does not know any better and was simply following instructions. He goes on to tell Jonas that release has always involved taking a person's life, whether they were old, had a birth defect, or they broke the rules three times. That night, Jonas stays at the Giver's dwelling and they formulate a plan to change the community for the better.