Your definition of forgiveness asks too much of the one forgiving. You go so far as to say that as one forgives, then he offers love to the one who was unfair. My response is, “No way.” I am not going to love the one who was cruel to me. What do you think?
There is a difference, in Aristotelian philosophy, between what a particular moral virtue is in truth and on its highest level (its Essence) compared with how we express that moral virtue in our own imperfect thoughts, feelings, and actions (in what is called Existence). Even though loving the one who offended you is part of the Essence of forgiving, this may not be attainable for you right now (in the Existence of your forgiving right now). This does not make you a failure. Further, it does not mean that forgiveness has overstepped its bounds by being connected with loving those (aiding them even when it is difficult to do so) who do not love us. Loving the other in this way is a goal that you might or might not be able to attain in Existence. Yet, this does not diminish the Essence of what forgiveness is in truth.