What had not been included in Rosemary's training in The Giver? Why hasn't The Giver given her those memories?

The Giver did not give Rosemary memories of pain in the beginning of her training because he could not bear to hurt her.

During Jonas’s training as Receiver of Memory, he learns that his predecessor’s name was Rosemary.  Rosemary is unique in that she failed her training.  She was replaced after a few years with Jonas.  As Jonas proceeds with his own training, he learns why Rosemary’s failed.  She meant so much to The Giver that he only gave her positive memories.  The result that when she first saw a painful one, she released herself.

Jonas is a little baffled by the case of Rosemary.  During his Ceremony of Twelve he was told that his training would entail considerable pain.  His rules also stated that he could not take medicine for it, and he could not apply for release.  At first, Jonas had no idea why he would want to be released.  He later learned that the rule was in place because Rosemary asked to be released.

At first, The Giver only shares pleasant memories with Jonas.  Soon, though he adds pain.  Sometimes he shares a memory with Jonas at Jonas’s request, when the pain of the memory is unbearable for him.  The Giver confides in Jonas that he did not share painful memories regularly with Rosemary.

"It broke my heart, Jonas, to transfer pain to her. But it was my job. It was what I had to do, the way I've had to do it to you." (Ch. 18)

The Giver explains that he loved Rosemary, and Jonas learns the concept of love through the memories.  He forced himself to give her “anguish of many kinds” and it was enough.  Rosemary asked to be released and they let her.

At the time that Jonas hears this story, he does not know what release really means.  When he sees a release, which happens to be his father killing a newborn infant, he realizes that Rosemary died.

"Rosemary had only those five weeks worth, and most of them were good ones. But there were those few terrible memories, the ones that had overwhelmed her.” (Ch. 18)

The Giver admits to Jonas that Rosemary was his daughter.  She was related to him, just as Jonas is, but they had a deeper connection.  Rosemary clearly loved him, but she could not bear the pain.  She was brave enough to end her life when she realized how tragic her community really was.  She injected herself, and that was that.

Clearly The Giver realized after this incident that he would have to take a different route in training Jonas, and he slowly exposed him to pain before it could become too much.  However, he is also slowly introducing Jonas to the reality of the community.  Jonas and Rosemary both likely thought that they were living in a perfect world.  When they realized what was really happening, they were horrified.  Each reacted differently.  Rosemary committed suicide, and Jonas escaped in order to return the memories to the people and end the atrocities of their community.