It is the inductive kick caused by the collapsing magnetic field. The voltage spikes until current conducts one way or another sometimes damaging whatever gets in it's way. It is energy limited so the higher the voltage such as Richard's Zener, the faster the magnetic field will collapse faster. An anti-parallel diode or TVS near the solenoid is the easiest and usually the lowest noise way. Otherwise giving the current a path to flow to go will also work.
Beyond that, it is the physics of the solenoid that limit the operation. A fuel injector is a small, short throw, low mass solenoid designed for very fast operation. I think they get an assist for closing with the fuel pressure as well. Heavier solenoids with weaker return springs, a longer throw, and weaker magnetic force will take longer to open and close. A stronger return spring, and a higher current for pulling in the solenoid will help improve the speed.