Question

Briefly introduce social Darwinism and point out that there was opposition to this way of thinking

Answer 1

Darwinism was always opposed at almost every level for everything he said. Genius often runs into that problem. It probably was no consolation for him that he was not alone in opposition to his ideas. I always like to tell the story about the fact that Darwin was a divinity student. I think, but I'm not sure, that he actually had a parish for a very short time. He also thought if he found fossils that suggested related creatures to his classification system that happened quickly, he would gladly say evolution was wrong. He found no such quick relationship. I admire his wife particularly, who was very devout (more so than he was). It was she who insisted he publish his findings.

Enough blab. I'm just very fond of Mr. and Mrs. Darwin.

Social Darwinism applies the survival of the fittest to the evolution to human behavior (mostly moral behaviour). 

Who opposed it? Almost everyone. Social behaviourists because they thought though the idea acceptable, it did not go far enough. Needless to say religious people then and even today are horrified that God is left out of the equation.

You can see a wonderful film starring Spencer Tracy and Fredric March called Inherit the Wind which was based on the Snopes Case. It was one of the most attention getting legal cases of its generation (1925) I'm pointing out all of this to show where the opposition came from. It had then in 1925 a long history of more than 50 years of being opposed. The church I go to vehemently opposes Darwinism in any form and it is now 93 years after the Snopes Case. and more than a century since the publication of Darwin's original book.

I'm sorry this answer is so long. Had you just asked what it was, you would have gotten a single sentence answer. Since you asked who opposed it, you get much more.