I don't think your question needs quantum physics to explain it.

Consider the case of a free electron plasma in thermal equilibrium. By the Bohr-van Leeuwen theorem, there cannot be a net magnetic moment for the plasma in equilibrium. Now turn on a magnetic field. The system will leave equilibrium and will generate a current opposing the magnetic field (I.e. Faraday's law). This finite current implies a net magnetic moment, meaning the plasma is diamagnetic.

Now ask yourself, "Why is then that in absence of an external magnetic field, the macroscopic magnetization is zero?"

  The answer boils down to the theorem I mentioned before, which is purely classical. There are subtleties in strongly quantum regimes (Quantum Hall physics for example), however.

I don't think your question needs quantum physics to explain it.

First of all, all materials do have diamagnetic contributions, and generically that is independent of whether intrinsic magnetic moments exist or not; all you need is charge. Even Quantum treatments (as done by Langevin or Landau for example) do not require pre-existing magnetic moments.

Consider the case of a free electron plasma in thermal equilibrium. By the Bohr-van Leeuwen theorem, there cannot be a net magnetic moment for the plasma in equilibrium. Now turn on a magnetic field. The system will leave equilibrium and will generate a current opposing the magnetic field (I.e. Faraday's law). This finite current implies a net magnetic moment, meaning the plasma is diamagnetic.

If one were to ask in this situation, "Why is then that in absence of an external magnetic field, the macroscopic magnetization is zero?" The answer is that there was no reason for moments to line up (no exchange interaction, etc.)