I don't know the texts you went over in class; however, I think I know what Darwin meant. I would defend his statement, and I will tell you why. He states that "man’s sense of moral conscience is by far the most important". Unless you believe "lower animals" have a conscience and the ability to reason/think, then you'd too agree that only man has the capacity to think/reason. Because man has a conscience--the ability to sense right from wrong--they're able to make decisions. Thus, having self autonomy. Because of this, man isn't an animal. They don't follow instinct but their "gut". Animals act out of nature. Man acts out on reason. (Of course, each reason is personal).
-I hope this was able to help you. An interesting topic this one.