I think sometimes it's easy for us as parents - or just people in general - to underestimate the amount of compassion a child can express. Children, as a rule, are selfish creatures. I don't mean that as a judgment, I mean it as a general observation. They think of their needs, their wants, their happiness. Over time they learn more and more to think of others ("How would you feel if your friend said that to you? Sad? So how do you think she feels now that you said it to her? Exactly!") but it's a work in progress.
All I have to do is observe my oldest daughter with her younger sister and I can easily assume that there's not much in the way of compassion or empathy there. The amount of bickering over "don't touch my stuff" is unbelievable. And also headache-inducing.