I think that compassion is different from feeling sorry for someone.
When you have compassion, your heart feels for them. Perhaps you want to do something for them to ease their suffering.
On the other hand, when you FEEL SORRY for them, you approach them with the attitude that they are unable to care for themselves. It is actually an insult. I have always had this "feel sorry for others" attitude and I know I got this from growing up in an alcoholic home. I have had to learn that this attitude is actually one that says, "I am better, more capable, than you." I have had to learn to allow others the DIGNITY to manage their own lives the way they see fit, to make their own decisions, without me thinking they need my help, rushing in and taking over.