My opinion is that arm circles are overrated.
A good strong arm circle certainly helps some kids to get a better punch on the board and/or a better block, but it's peripheral, if that makes sense.
I'd compare arm circle technique to head position in a giant on bars. Many coaches teach kids to keep their head in while going over top on the giant, because it helps the kid stay hollow. Does that mean that having the head in is necessary or should be judged? No. It's not the head position that makes the giant, it's the body position; the head just helps some kids for some reason.
An arm circle on vault is similar. It is helpful to some kids, but it is not an integral part of the skill.
I don't know the specifics of the girl's code as well as I know the guys code. However, in my opinion, the arm circle should not be judged for either boys or girls, as many of the best vaulters in the world have no arm circle at all.
I generally don't stress much about arm circles; some kids do it, some kids don't, and I let them do whatever they're comfortable with.
One more thing, though:
The reason I ask is that we were at a meet this weekend and our girls' vault scores were low. Another coach said the reason was that this particular judge was taking off if the girls did NOT do an arm circle. It is not in the text, but just preference of that judge, I guess.
I really really
really hate when judges do this; unfortunately, it seems to be an endemic problem on the women's side of the sport (less common on the men's side, though far from nonexistant). The judge should not be allowed to make stuff up that isn't in the code; their job isn't to write the code, it's to score according to it. If you can't judge according to the code, you're not qualified to be a judge and should not be given the job, in my opinion.
Sorry, that's just an enormous pet peeve of mine.