Of course reason has enemies, reality sometimes is really hard to believe; sometimes we simply don't want to.
For some reasons, human beings need to believe everything has a meaning. We are struggling every day to find meaning to our lives. Reason is of course a way to find meaning of things, of natural phenomena, for example. What human mind can't really easily accept is that certain things happen just for a coincidence. It is something scary, because we can't have control over chance. And we want to be in control of everything. We want to see order and meaning, we are so scared of the unknown that our minds is willing to believe literally everything, from tea leaves to stones, from planet positions to people charmingly claiming to have paranormal powers. Can all these believes be harmful?
History have taught that people that have strong believes that go against reason have the tendency to impose them on others, usually in very violent ways. Dawkins, at the beginning of the video, says something very important: that we live in dangerous times when superstitions is gaining ground and rational science is under attack. That makes me think of the Medieval times, when superstitions had many fellows and the scientists were persecuted. Is this happening again? I don't think that the situation is now as bad as it was, but yes, superstions and believes can be harmful: let's just think of all the people that spend lots of money and become addicted to this "magician" that claim to solve their problems.