That's a standard emergency instruction. Not only would you be unable to help a kid if you're passed out from lack of oxygen, but I think there's also concern that a kid could resist the mask and perhaps be less inclined to do so if the child first sees a parent modeling the behavior.

Maybe it's just in movies, but if a FA needs to walk the aisle during emergency conditions, the protocol might be to switch from one of the "extra" masks to the next one as he/she progresses along the length of the aircraft. Or maybe this is fiction and there are fully detached portable sources of oxygen for crew to use in emergencies.