To me it is irrational to forgive. You are saying that you are not mad when in fact you are. So, forgiveness is a shell game, a kind of illusion or magic trick in which one wishes away the anger and internal discontent and then, presto, all of this is gone. Sorry, but I can’t accept this magic trick that you call forgiving.
I think the illusion actually is your belief that forgiveness is a trick. Is it a trick when randomized experimental and control group clinical trials show that as people take the time to forgive, their anger, anxiety, and even depression can go statistically below clinical levels and remain low months or even a year after treatment? Science done well is not a shell game. I urge you to look at the science. One place to start is the book for mental health professionals, Forgiveness Therapy, by Enright and Fitzgibbons (2015, American Psychological Association).
For additional information, see Forgiveness Research.