That levitation is based on their being a large field gradient (diamagnetic levitation is based on the field gradient), so you could not do the same for a human.
Do you have a source for this? I don't believe it is true. Diamagnetism is a fundamental quantum mechanical property related to the quantum mechanical analog to the Lorentz force. Spin 1/2 electrons have exactly 2 states: opposing or attracting a static magnetic field, regardless of direction of the field or orientation of the particle.
When all electrons are paired (and the spin fields cancel), all that is left is that Lorentz force and you get diamagnetism. Otherwise, you generally get paramagnetism (attractive because of the net dipole created by net spin).
The energy of a diamagnetic material is lower in a lower magnetic field, so there's a force pushing it away from higher fields. This force is proportional to the gradient of the field. In a constant magnetic field, there will be no change in energy and so no force on the diamagnetic material.
That is the 1800's classical explanation of electric charge, which is not consistent with experiments, nor does it line up with magnetism, which is inherently quantum.
1. Even in your classical description, what you just described (following field lines) does not require there to be a gradient. If there is a gradient, yes, the forces will follow it. But there is still a force in a static infinite applied field, and potential energies still change as things move.
2. Diamagnetism is a quantum property, not a classical one. It exists due to the polarity of spins in an electron pair (although frankly, this explanation is weak and magnetism is one of the less understood subjects in physics). Even if a macroscopic field has a gradient, it will look like a static field at the scale of an atom, at which scale diamagnetic forces exist.
1. Yes, a gradient is required. If the energy of the diamagnetic material does not change, there cannot be a force, as this will violate conservation of energy. You are proposing a perpetual motion machine of the first kind.
2. The quantum nature of diamagnetism doesn't matter in the slightest to the argument being made, so why are you bringing this up?
I do believe I was mistaken in my original post and that a locally constant magnetic field will not produce an appreciable diamagnetic force.
Diamagnetism works by inducing dipoles in the medium, and
a dipole placed in a constant field experiences no net force. It may experience a torque if it is not aligned with the field, but in the case of diamagnetism the induced dipoles are naturally aligned, and so there is neither force nor torque.
Let us consider an experiment. Take a long cylindrical coil, so that in most of the coil the magnetic field is constant. In the center, place a diamagnetic material. Does it experience a force toward either end of the coil? If not, why not, according to your reasoning? If so, why does it experience a force toward that end of the coil and not the other?
I misinterpreted your point due to my own misunderstanding of quantum spin, a subject I'm currently studying. I see your point now, due to the dipole nature of magnetism, and the confusion came from the original "so you could not do the same for a human," in which I think you meant "you could not do the same in a perfectly uniform field."
You could not do it to a human because you'd need a nonuniform field over a much larger distance, which means the maximum of that field would have to be enormous, far higher than in the frog case, and far higher than could be generated by any practical electromagnet, superconducting or otherwise.
