I was going to answer, but it looks like TPCShauna beat me to it. Since they are not claiming to be Christian, why not just take the name out to make it more of a generalized Oath? One that is acceptable to everyone? I don't know, it just makes sense to me.
It makes sense to me, too, but I bet it would cause a much, much, bigger uproar than the Girl Scouts just letting each person decide whether to skip or replace it individually. That's always the big argument against taking "under God" out of the pledge of allegience. "
People who don't want to say it can just skip that part."
GSA has decided to make it almost impossible for someone to volunteer and help a troop or be a leader. They have got certification crazy and paper trail crazy. Everything you want to do has to be done with one of their trained "leaders" there. You would not be able to teach them archery unless their leader had attended about 12 hours of training. You can not even take the girls to a nature center and have a fire in a fire ring(you know like you have in the backyard) with out attending approximately 2 days of training. To camp the leader has to have attended their training that isn't held that often and I'm not sure if it is overnight but it does run 2 days. And I don't mean going out into the wilderness, this is for staying overnight at a campground. For a camping trip you need a first aid person and that means their training again and no a trained paramedic doesn't count unless they had their training. Many leaders do not have time to attend 3-6 different training sessions just to take the girls overnight so the troops do not get to do it. This is on top of the regular training that you need to attend just to be a leader. So they do things with the girls that don't require all the additional training.
Hmm, it must differ by council, because our training situation isn't that cumbersome. The classes are always 3-3.5 hours each, never a full day, are offered pretty regularly in various locations and many can be done via home study instead of sitting in a classroom

(my fave way to do it!). Archery and horseback riding have minimum age requirements and requirements for instructors, but no leader training is required.
For overnights and camping, there are progressive classes based on where the troop is going. I can see where it could be overwhelming if a new leader starts with an older troop who is ready to camp outdoors. Since I started with Daisies, it was no biggie. The classes relate to the suggested progression of skills which are designed to help the girls progress slowly, from simply being away from mom and dad for a weekend, to learning to cook over a fire, to planning a trip farther away from home.
When you're with the troop for a while and you start them off slowly, it's just about a class a year, so no biggie, but like I said, I can see if you're stepping in to take over an older troop, you'd need to take a lot of classes, since each level of class is a prerequisite for the next.
Oh, and if the leader can't find the time to take the training, the troop can always do a mother-daughter or family camping trip. No training is required if each of the girls have a mom or dad there.