What can we learn from this? Well I beleive a few things.
1) At least there are still people out there who do not want to take moral relativism to its logical conclusion. This is a good sign because it shows that people's hearts are not totally blackened yet. Truly if you believe there is no God then everything is permissible. Thus their conscience is not yet seared to the point of no return.
2) Richard Dawkins still believes in a moral code. Why would he come out and apologize for his comments? If he really doesn't believe in a god then who cares about 'tact' or 'understanding'? To be honest, if there is no god then who cares if we kill the babies?
3) Moral Relativism is atrocious. Most people who like to claim morals are relative only do so to justify their sin. But when we take it all the way home we get statements like what Dawkins said above. It is good to see that people balked at his comments but in reality they shouldn't. If they too believe morals are relative then they cannot, by their own standard (or lack their of), claim what he said is 'wrong'. But it is good to see that it is an atheist, and a world renowned one at that, prove that moral relativism moves a culture into sickening situations. This story is a great example to use for people to awaken their conscious. You can start a conversation by asking them if they think Richard's comments are right or wrong, good or bad, true or not true, etc... If they don't like what he said then you can point out that is because they know inherinetly that there is a standard. This standard being the Law God wrote on their heart. You can also point out the absurdity of believing in moral relativism because they would have to accept his statements even though they instinctively reject them.
In the end atheism must believe in moral relativism and relativism is just not practical or appealing. I am glad to see that people on social media rejected Dawkins' comments. Now it is our job to show them why they reject them...because they believe in an absolute moral standard which can only be grounded in God.