Unconstitutional

The US "Pledge of Allegiance" goes like this:

I pledge allegiance to the Flag of the United States of America, and to the Republic for which it stands: one Nation under God, indivisible, with Liberty and Justice for all.

It's been ruled unconstitutional because of the words "under God" and the separation of church and state thing.  Could someone please explain the separation thing?  I thought it was to keep the government out of the church, not keep the church out of everything else.  Much silliness.  I think a few people have a little too much time on their hands.