One thing I always discussed was what “down” means exactly. Start by asking students which direction is “down”? (Most students will point toward the floor.) Expand on this by asking what someone in Australia would say. Are they pointing in the same direction as you? End up by emphasizing that “down” means “toward the center of the Earth.” I would not recommend saying that the force of gravity due to the Earth doesn’t pull “down.” It does.
You can use this phrase, but you need to emphasize that the reason the ground is falling away from the orbiting object is because the object has sufficient tangential (sideways) velocity.