Conservative evangelical Christians believe that evolutionary theory is incompatible with morality, civilization, and of course Christianity. They have no serious scientific arguments to make against evolution, so it's most common to see them offering religious, social, and moral arguments against it. They don't seem to realize that even if all of these arguments were valid, they wouldn't constitute good reasons to pretend that evolution isn't true.
One popular anti-evolution argument is a moral one. According to the Christian Right, evolution teaches that we humans are ultimately descended from animals rather than that we are special beings created in the image of God. When people believe that God created them specially and that humans are images of God, they are supposedly encouraged to behave more like God wants them. If kids believe that they are simply another form of animal life, then they are supposedly encouraged to behave like animals. If kids believe that they are not a special product of divine will, then it is claimed that they will lose hope and stop caring about either their lives or the lives of others.
None of this really follows from evolutionary theory. At most, it only appears to follow because of the narrow and rigid nature of conservative evangelical Christianity. This form of Christianity justifies hope, civilization, and moral behavior on such limited and narrow terms that any deviation from the foundation leads to the collapse of the entire structure. Thus if there is a problem, it's not with evolution teaching that humans are descended from other animals, but rather than conservative Christians cannot come up with any reason for moral behavior other than the idea that humans were specially created in the image of God and separate from other animals.
The above poster was created by the German government during World War I and said 'Elend und Untergang folgen der Anarchie' (Misery and Destruction follow Anarchy). Depicted is an anarchist monster carrying a knife and a gun. The original was an attempt to urge people not to give in to anarchist criticisms of the war of the German government. I have replaced the text with the standard canard about the teaching of evolution or Darwinism leading to immoral, even bestial, behavior.