It is in Chapter 18 that Jonas first finds out the story of his predecessor, Rosemary, which had been shrouded in such secrecy and mystery. In telling Jonas what happened, the Giver is quick to identify comparisons between Jonas and Rosemary: both wanted to experience "everything", and both knew it was their "responsibility" to bear more difficult memories. After the first painful memory that the Giver gave her, she appeared "stunned" at the end, and after that it was all different. It was her inability to cope with and accept these difficult memories of humanity's past that made her decide to request release.
It is interesting that Jonas explicitly implies that Rosemary was not brave enough to be the next Giver. It is important to bear in mind the Giver's response after he has shown Jonas what his father really did with the twins:
"You suggested, Jonas, that perhaps she wasn't brave enough? I don't know about bravery: what it is, what it means. I do know that I sat here numb with horror. Wretched with helplessness. And I listened as Rosemary told them that she would prefer to inject herself."
Clearly, Rosemary showed great bravery in freely accepting, and self-administering, the "Release" that she wanted to forget all the painful memories she had received.
In Chapter 18, the Giver explains to Jonas what happened to the last Receiver, who was named Rosemary. Rosemary was the Giver's daughter, and for the first five weeks of her training he only gave her positive memories. After the fifth week, the Giver began transferring memories of loneliness and loss. The Giver could tell that the difficult memories had a powerful impact on Rosemary, but she urged him to continue transferring the negative memories. Since the Giver couldn't bring himself to transfer memories of physical pain to Rosemary, he gave her poverty, hunger, and terror. These difficult, painful memories were too much for Rosemary to handle, and she requested to be "released." When Rosemary died, her negative memories were released into society, and the community experienced her anguish.
In my opinion, Rosemary was brave because she continued to ask for painful memories throughout her training. She understood that it was her duty to receive those negative memories, but she could not bear the weight of the world's ills, which is why she asked to be "released."