No, it's destroying the idea of forgetfulness and it's been doing it since books. Forgiveness takes an active effort, whereas forgetfulness is passive. The former is probably a virtue and the latter probably a vice (if you can help it).

Let's forgive but not forget, we need those lessons.

No, it is destroying the idea of forgiveness. The article gives the example of how data mining could be used to target individuals who an algorithm predicts could be likely criminals. This paves the way for discrimination and removes the presumption of innocence our criminal justice system is (should) be built upon. The criminal justice system is already unforgiving enough as it is.

The article didn't mention it, but the self-righteous outrage mobs that have become common since the rise of social media is also greatly destroying the idea of forgiveness. Once your reputation is destroyed by the social media mob, you face an incredible uphill climb to restore it.