I have heard that forgiveness is not a moral virtue but instead is a psychological skill in which a person reduces resentment toward an offender.  Why do you call it a moral virtue?

All moral virtues are concerned with goodness toward others.  For example, justice is to be fair to others.  When we forgive, at least on its highest level (whether or not a particular person reaches this level), we are offering kindness, respect, and even love toward those who have been unfair to us as forgivers.  Given this willed goodness toward an offending person, this is a quintessential sign of goodness. If forgiveness is only being less resentful toward an offending person, this could be achieved, for example, by seeing that person as so less than human that you feel sorry for this person, thus reducing resentment.  This seems too narrow and reductionistic.