The forgiveness the meme is about is the one of God and Jesus Christ for your sins and the price for those sins: eternal death and suffering in hell when you die on earth. We're not talking about men forgiving men. Jesus Christ certainly did show that we should forgive but he has shown that people should sin less. The Bible agrees with you on the "never forget" point. Non-religious opinion about men forgiving others: to forgive is a good thing for yourself (it frees your heart and mind of negative thoughts) and it does not necessarily cancel any form of retributive justice. And even if you believe those are not compatible, remember that one man forgiving does not mean others won't do justice for you or against your enemies.