I don’t know much about Kadampa Buddhism, but this teaching about compassion comes from a page at a Kadampa site called “About Dharma,” and I like how it lays out so simply WHY we need to WORK on our practice of compassion for all beings:
When our family and friends are suffering we easily develop compassion for them, but we find it far more difficult to feel sympathy for people we find unpleasant or for strangers. Furthermore, we feel compassion for those who are experiencing manifest pain, but not for those who are enjoying good conditions, and especially not for those who are engaging in harmful actions. If we genuinely want to realize our potential by attaining full enlightenment we need to increase the scope of our compassion until it embraces all living beings without exception, just as a loving mother feels compassion for all her children irrespective of whether they are behaving well or badly. This universal compassion is the heart of Mahayana Buddhism.
Now, if you still have a little time to spare, read this short-short story, Tears in the Rain, from the blog “Zen Moments.” It shows us how powerful compassion can be, and how just the smallest action we take can mean so much to another person.