special relativity - Why does the minus sign in the Minkowski metric mean that nothing can move backwards in time?

I just watched this video:

http://www.youtube.com/watch?v=GkCWywO93b8#t=27

and there Mr. Cox states that because of the minus sign in the Minkowski metric nothing can move backwards in time. It's the first time I hear this argument and does anyone know how to show this?

To be precise: I'm looking for an explicit computation that shows why the minus sign in the Minkowski metric means that we can't rotate into a frame where $t \rightarrow -t$