Been to college camps and almost all teach you Keep It Own. In response to why not take it off. As a coach I have seen many catcher's step on it, as the ball floats back where they dropped it. Twisted ankle. Lose the ball as they take the mask off. Just 2 good reasons.
I always want my catchers to keep thier mask on. With the newer style masks and the visibility they provide... There's no good argument to remove it. There is however, a very good argument for leaving it on. See the attached picture.
Mike Candrea stresses to coaches to teach catchers to keep the hockey style masks ON!
(saying that, I've watched Cali Balko when playing at U of A remove hers, but thats because of years of habit.)
I am a catcher and was taught to take the helmet off. By taking the helmet off you will be able to locate the ball better and when you retrieve the ball you will be able to see the whole field much better. When you still have the helmet on and you turn around with the ball you feel panicky and under a lot of pressure to make a play.....but if you have the helmet off, you are much more calmer.