When the angel comes to Mary and the shepherds both, it tells them not to be afraid. Usually, I think, the fear in question is interpreted as the fear of the angel. If we take these events literally (and I'm not saying we shouldn't), a manifestation of the divine right in front of you would be a pretty scary thing. But John Carrol, in a blog post for Baptist News Global, points out that that's probably not the only fear the angel is talking about.
Carrol uses an interesting metaphor to explain the problem of fear--it's like an anti-virus program for your computer. And so, in an age of constant viral threat, it's a useful thing to have. But most of us have probably had certain antivirus software (not to name any names) that didn't seem to protect our computers as much as they seemed to TAKE OVER. They can gum up the works, constantly asking us to approve websites we visit, files we download, slowing our computers down because they are always running at full steam. Fear is like that. When it takes over, we are no longer in charge, no longer capable of using our best, moral, judgement. As a society, it is past time to switch to some new software.