many people who have this reaction I find have done spinning in aircraft that are not really suitable such as C152 or Pa28 or an instructor who uses the technique that results from learning on these aircraft, by this I mean that they pull hard into the entry then have a rushed patter before the aircraft recovers by itself - do spinning on a proper spinning aircraft with a good instructor
C152s and PA28s spin and recover in a way which allows the student to appreciate the concept of a spin, and the sensations to be experienced. These types also allow practice at recovery technique. They are suitable. That is not to say they are the best, but they're suitable - they're certified for it.
A good friend of mine used to tell me about spinning Meteors, Hunters, and the efforts made to not spin Phantoms. From what he tells me, spinning a Hunter made a pilot out of you - a Hunter pilot. Very cool, but personally, I don't see myself needing to develop the skills to spin and recover a Hunter.
If a pilot learns to skillfully spin and recover a C152, or a PA28, that pilot will have adequate skills to recover a recoverable spin in any certified single engine aircraft, and that's all that's intended from the training.
Sure, there are excellent things to be learned in aerobatics courses, and in other aerobatic types - go for it if that interests you.
But otherwise every student should learn the basics of spinning - three reasons: Awareness - you know what's going to happen if you get in, and that there will be a period of rotation where the aircraft will seem to not react to a control input, but be patient. The knowledge that you can recover a recoverable spin, so don't just give up. And, you understand the sensations as you approach the stall/spin, so you can allow yourself to get close (a confident 1.3Vs approach in a crosswind with a chop), and thus fly the aircraft as it was designed, rather that these 1.3Vs + 15 knot approaches resulting from lack of skill and understanding. An added bonus would be the instructor who has the student spin the same aircraft at the extremes of its spin approved C of G range, to see the difference in handling.
This is where one learns why we don't load behind the aft C of G limit!
I'm one of those students of the '70's who was only trained spins in a 150. At that time, that was all that was available. But I practiced, practiced, and still practice. I do not accidentally spin airplanes, and when I deliberately spin them under planned safe testing conditions, it works out fine. Now, I count 12 types I have spun, and with changed configurations, it becomes 17, With the biggest being a Cessna Grand Caravan. It taught me that there is no room to not follow the Flight Manual procedure, so know your aircraft!
So students, go and spin the spin approved aircraft - even just the compromise C 152/PA28, in a planned flight for that purpose, with your instructor. You'll thank yourself later....