You make a good point about anger sometimes becoming part of one’s identity. Also, at times people are fearful of confronting their own anger because they fear an inability to be rid of this. Yet, once a person realizes that forgiveness is a kind of safety net for the unhealthy anger, they tend to go ahead with forgiveness because they have more confidence in their ability to eliminate this excessive anger.
Also, with regard to the theme of identity, people can transform their identity, from resentful persons to persons who are caring and who do not let others’ injustices define who they are. If you see receptivity in your father regarding forgiveness, you might want to talk to him about these two themes: a) forgiving is a safety net for his anger and thus that anger will not overwhelm him if he starts to look at his own father’s behavior; and, b) his identity might change in a positive way.
For additional information, see Learning to Forgive Others.