Believe me: I think I know my feelings pretty well. But I also claim that they are often so much different from the feelings other people have that this does not help me to empathize. Just to give one example: How is the feeling called that you feel when you read and understand beautiful mathematical proofs? I have not found a name for this feeling in any psychology book that I have read. On the other hand grief (in the sense of the feeling that people feel when someone near dies; I hope this is the intended translation of the German word "Trauer" - I'm no English native speaker) is a feeling that I only know from literature and watching people - I can confidently say that I never felt such a feeling myself.
Back to topic: I believe the step from "knowing your own feelings" to "empathy" assumes that your feelings are somehow related to the feelings other people feel. I think this bold assumption does not hold very strongly for me. Believe me: If I act on this assumption, chaos will happen. On the other hand if I apply, say, some maximum-likelihood estimation (to use a word from statistics, don't interpret the word "maximum-likelihood" too literally) on how another person might feel (which is often quite the opposite to how I feel and completely against my instincts and I would never like to be treated this way), at least less chaos will happen.