Forgiveness is a way to show your love to someone else, but forgetting is showing yourself love. Forgive and forget so that you can continue to balance your life in harmony. Forgiving and forgetting is a part of our life. The emotions created thru forgiving and forgetting is a part of the cycle that brings peace and harmony. In deeper terms it also defines the whole giving and receiving aspect in life.
I'm not talking about the whole show about giving and receiving material things too. Nice cars and houses do not put me at ease or at peace. It'll only make me worry more with bills, keeping up with maintenance, and all that is attached to it and I rather not have those things. I could also by my love the world, and still I question, would he do the same for me. Of course if I ask...he'll say yes....but as you note, it still leaves room for doubting...and if you doubt things too long...you won't be happy.
To me, to have harmony and peace, is to share with one another your energy. Forgiving and forgetting is nothing materialistic, but it energy because it is a feeling. It's main primary emotional trigger is, Love. And love is a BIG part of us...our life.
So I forgive those that hurt me because I love them and I forget about it because I love myself, I only want that positive energy in me, I don't want to dwell or hold anything against anyone because i need that flow to continue so that my life can be balanced.