When skydiver nellie opens her parachute, the air drag pushing the chute upward is stronger than earth's force of gravity pulling her downward. a friend says this means she should start moving upward?

No, the skydiver does not start moving upward. Yes, initially the air drag is stronger than the weight, and so there is a net force pushing upward, and the result of this force (because of F=ma) is a deceleration of the skydiver (because the force goes against the direction of motion). However, the air drag is proportional to , the square of the velocity. Thus, as the velocity of the skydiver decreases, so does the air drag, and eventually the air drag becomes smaller than the weight. So the skydiver continues his motion towards the ground.