I read in a Mountain bike book that supposedly you should avoid "crossing the chain" when shifting.

According to this book, "crossing the chain" occurs either when you are on the top-most chain ring in front, and the top-two gear sprockets in the back, or on the bottom-most chain ring in front, and the bottom-most gear sprocket in the back.

I know for a fact I have done this.

Is it harmfull to the shifting system?

I do notice when I am on the middle or lowest front chain ring and the bottom-most gear sprocket, I hear a little bit of noise from my chain - I thought the chain just needed to be tightened.

What is the theory behind this?

Thanks!