He who receives kindness should never forget it,
but he who performs it should never remember it.
We should always be grateful for the kindness that others show towards us. Kindness can relieve our fears and worries, and lessen our suffering. Remembering the kindness of others, we will be more inclined to pass the kindness on because we know how much it meant to us.
But why should we not remember when we are kind to others?
Thinking of our kindness to others can result in our looking down on the person who needed our help. Feelings of superiority can arise as we mentally pat ourselves on the shoulder and the other on her head, like we would a child. There goes our regarding all beings equally.
As we dwell on our good actions, we tend to congratulate ourselves. Unaware of what is happening, we allow pride to creep in. And there goes our humility. The Buddha warned us of the four poisons of greed, anger, ignorance, and arrogance. Even a touch of pride is arrogance. So just as we need to guard against any rising of anger or craving, we need to also guard against pride.
With our act of kindness, we laid the foundation for the future enjoyment of some good fortune. Ideally, we will want to use our good fortune to continue helping others. But if we ourselves enjoy our good fortune, for example by feeling even a trace of pride, we reduce that good fortune. So it is much better to dwell on thoughts of the kindness of others and to let go of memories of our own kindness.