In general there are a few aircraft types (cannot recall names) which will never recover from a spin. On the other hand trainer aircraft are designed to recover predictably from a spin so that pilots experience the frightening and disorientating feeling of a spin and still have their wits about them to either conduct what needs to be done to recover, or if that does not work, eject appropriately.
Trainer aircraft must stall, spin and recover predictably.
Here is a fantastic article by Air Marshal Rajkumar about test flying the Alpha Jet and Hawk long before the AJT came and their stall/spin characteristics
Read it all - but here is a quote
The Hawk did not want to spin and one had to sit with prospin controls applied for several seconds before she dipped the nose and settled into what appeared to be a steep nose down corkscrew motion. Standard application of anti spin controls ensured quick recovery. After the Alpha Jet experience this was an unimpressive spin.