How can diamagnetism levitate anything?

From the explanation of diamagnetism that I was given, the electrons when exposed to a changing magnetic field will change their spin in accordance to Lenz's law. This will induce an opposing magnetic field and thus repel the magnetic field.

However, if this was the explanation, then why can people levitate frogs in solenoids? If the current in the solenoids isn't changing (is not AC) then there should be no change in flux over time and hence will not induce current and hence will not induce an opposing magnetic field. Thus the frog should levitate briefly and then go splat.

Could someone explain how diamagnetism can levitate a frog then? I suspect the above explanation might not be correct but I couldn't find anything else.