Darwin is not a Social Darwinist

Two weeks ago we had a lecture by Dr. Bruce Alexander. I felt that this was one of the more interesting lectures I've seen in a long time. As a Darwinist, Dr. Alexander explained some of the views of Darwin in response to many of the critiques of Darwin that we’ve seen to date in our class. He went on to explain some common mistakes people make when referring to Darwin or trying to understand Darwin. One of his most important points was that Darwin was not a Social Darwinist which, at first, I found surprising. I did not realize that Darwin himself could not be a Darwinist because a Darwinist is someone who promotes Darwin and he cannot promote himself. I found this concept a bit confusing but once I understood it I found it to be very interesting.
I really like the idea of group selection which was one of the topics that Dr. Alexander brought up. He said it was almost dismissed by most scientists and social scientists. Groups of cooperative people are constantly at war said Dr. Alexander. This seems contradictory since cooperation means getting along and war means not getting along I suppose. If one group of humans selects to eliminate another group then traits are still being extinct. Why would we want to eliminate some qualities that only exist in some groups? Why would we want pure bred things? If we are so concerned with being the best and most powerful and smartest, why wouldn't we want to have certain traits from different groups and breed them together to combine their assets.