There are a few decent rules of thumb for para- and diamagnetism.
A system is paramagnetic if it has a net magnetic moment because it has electrons of like (parallel) spins. These are often called triplet (or higher) states. In atoms and molecules, they occur when the highest occupied atomic/molecular orbital is not full (degeneracy > 2 * # of valence electrons). In this case, Hund's rules suggest that the electrons lower their energy by aligning their spins.
In contrast, a diamagnet has no magnetic moment because all electrons are paired.
Nearly all free atoms are paramagnetic because nearly all atoms have unpaired spins. The exceptions are the the last column of the s, p, d, and f block (2, 12, and 18). (Any that I'm missing?) For instance, that's an important property for the Stern-Gerlach experiments and magnetic trapping.
Most molecules, however, have fully paired spins. First off, most molecules have an even number of spins, except for free radicals, which are relatively unstable. To figure out if the molecule has a net magnetic moment (paramagnetic) or not (diamagnetic), you need to look at its molecular orbitals. The classical example is oxygen, which has a half-full (or half-empty) $\pi_{2p}^\ast$ orbitals, and nitrogen, which has a full $\pi_{2p}^\ast$ orbital. See: http://www.mpcfaculty.net/mark_bishop/molecular_orbital_theory.htm.
For crystals and solid-state materials, the question is more challenging, but it ends up coming down to the same question: is there a net magnetic moment because of unpaired spins, in which case it's a paramagnetic? or is there no net magnetic moment because all spins are paired, in which case it's a diamagnet?
Of course, in solid-state, there is a third situation, a ferromagnet. This is rather difficult to predict in real systems and is a major field of research. Some model systems (model system: a much simplefr mathematical model of a system) are solvable and give hints of what to look for. For instance, free spins in a lattice create a paramagnet by the argument above: the crystal has a net magnetic moment. You expect, in a magnetic field, the spin of one electron creates a magnetic field that can effect its neighbors. Since the system is paramagnetic, you might expect that the neighbors align with their local magnetic field, which is induced by their neighbors, and the whole crystal polarizes itself, creating a ferromagnet. This explanation is a mean-field Ising model. It gives a good intuition even though it's too simple to describe any real system.
Initially, due to acceleration of the magnet the rate of changing of linked flux ($-d\phi /dt$ is itself changing and hence the induced emf, and the force due to it, is increasing (changing). Ultimately at a sufficiently high velocity, the force due to induced current will be equal to the weight. When $F=mg$, then the net force and hence acceleration is zero, but the flux is still changing if it has a non zero velocity. After this, since velocity is constant and no acceleration exists, the induced emf will be constant because $-d\phi /dt$ is constant due to constant velocity. This means the forces will no longer vary and the magnet will continue with same speed.
Your analysis assumed the force due to induced emf to still change after $F=mg$ but that is incorrect as constant velocity will cause constant induced force, in the perfectly long tube's case.
Best Answer
The fictitious current loops are permanent in that the current in a loop does not change with time unless an external influence is present.
In this case the external influence is an external magnetic field being switched on.
When the external magnetic field is changing an electric field is induced in the loop (Faraday) which accelerates (either positive of negative) the electron which is moving in the loop.
When the external magnetic field reaches a constant value then there is no longer an electric field accelerating the electron and the electron now moves around the loop at its new speed.
So the external magnetic field in changing from zero to a constant value has changed the speed of an electron moving in a loop from a constant initial value to a constant final value which is either larger or smaller than the initial value depending on the sense of the electron's rotation relative to the external magnetic field direction.
As is explained in the passage this results in some electrons moving slower and some electrons moving faster thus altering their magnetic dipole moments which results in a net downward magnetic moment if there has been an upward external field switched on.
You can demonstrate the levitation of a pencil lead at home.