Which school is that, Lady? I ask because spinning at 2400' really is dangerous. This should be taken further, especially as it is the head of training.
Beaver - have you never taken a PA-28 into a proper steep turn, i.e. over 60 degrees? It is not difficult to spin if you overcook the turn, and if this aircraft is all that is available (it is at one of the clubs I fly for) then teach recovery from incipient. I have had a student send us incipient in an aircraft not cleared for intentional spins from over-enthusiastic response to wing drop at the stall. It is also easy to spin from a glide if you let the speed bleed off stretching the approach. In one study I read "Stall and spin" was found to be the final cause of over 30% of fatal accidents! Most were perfectly survivable power losses.
I know very students who are really scared of spinning, and most of those are a lot happier once they have actually done some. They often get the fear from those that have never been taught or not taught thoroughly. They often pick up fear from people who themselves are scared, or who talk about spins without the required reassurance.