Because forgiving is a choice, not demanded in any society of which I am aware, you can set forgiveness aside. Yet, when deeply hurt by others, what is your alternative for ridding yourself of a gnawing resentment that could bring you down? In the giving of the compassion, in the bearing of the pain, in the attempt to be kind, the paradox is that you, yourself, may experience a cessation of the poison of that resentment. Does this seem like an outcome you would like to set aside? Forgiveness advances you toward this healthy outcome and may even reestablish a relationship if the other can be trusted and does not harm you.
For additional information, see Forgiveness Defined.