I have read in the psychological literature that forgiveness primarily is a motivation to offer goodness to those who hurt us. Is forgiveness primarily a motivation toward the good?
No, this idea that forgiveness primarily is a motivation is philosophical reductionism in which the writer takes one important part of forgiveness and blows it up so large that it takes over the entire spectrum of forgiveness. Here is why motivation is only one part of forgiveness: Suppose someone hurts you and you now are convinced that you should and will forgive. After that, you sit in your hammock, read your on-line messages, listen to music, and turn off all thoughts and actions regarding forgiveness, never to return to this. Have you forgiven? Of course not because you have not engaged in the difficult thoughts, feelings, and actions that make the forgiveness response more full, more accurate.