I think "forgiveness" is more about your own psychological wellbeing than anything else. If you cling to the hurt people do to you and hold hatred in your heart towards them, you are really only hurting yourself further. Hate is not a pleasant state of mind and prevents peace of mind and happiness.
It isn't even particularly Christian. It can also be found in Buddhism, Sikhism, Jainism, and many other religions, and is just sensible mental healthcare not requiring any religion at all.
That's not hard core Catholicism, that's hard core Christianity. I don't know how people can forgive unless they acquire the Holy Spirt within them. This is why He's known as the Comforter.