When I say it concerns me, I didn't mean I was frightened or thought I couldn't handle it, just that it could be a fright for the student.
Also thinking about inadvertent spins in a type not cleared for intentional spins, and the outcome being a very steep spiral. Recovery is simple enough, but I'd imagine it would be very easy to pull too hard and over stress something.
Glad to hear you are mostly concerned for the student, but really all this should have been covered in your FIC course! Yes, if a student gets that far it can be frightening for them, but the ONLY time they should be in this situation is when YOU are teaching it, if that is the case you should be putting it over in a way that it minimises their concerns! This is one reason spinning should be taught in an aircraft that spins properly, it can be done in (relatively) slow time and much calmer than in, say, a C152 where you are trying to get the words in before it degenerates into a spiral. Inadvertent spins are something you really should not be ending up with flying with students, unless maybe you are teaching aeros, in which case of course the a/c will be cleared for spinning anyway - YOU should be recognising that it is approaching and stepping in before it gets that far.