Theoritical issue in Electromagnetic induction

The article is following the direction of thought in this article. Namely, there are infinite object in the universe to be induced by any electromagnetic coil, thus it would take infinite energy to induce any electromagnetic coil, which is contrary to everyday experience. We can either resolve this by postulate that somewhere in the universe that has supplied this infinite amount of electrical energy, or we notice that the presence of ferromagnetic material near an electromagnetic coil reduce but not increase the inductance of the electromagnetic coil.
Now consider a common experience of a magnetized electromagnetic coil attracting nearby ferromagnetic metal. If we consider from the spring analogy of electromagnetism, then as the metal approach the electromagnetic coil, the strength of induced magnetic field in the metal would only increase in strength according to the cube of their distance and the velocity of approach. We can see metal as sort of passive string, which doesn’t have any inertia nor tendency to preserve its only electromagnetic field (or the tendency is so weak that we can effectively ignore it.) However, the electromagnetic coil is a structure that built to resist the change of electromagnetic field, therefore although the metal is passively influenced by electromagnetic coil, it nevertheless exert an influence to the electromagnetic coil. Thus, as the metal responding by increase the strength of magnetic field that is the opposite of the approaching electromagnetic coil. By Lenz's Law, we should expect the electromagnetic coil would react to this strengthening of electromagnetic field in the metal by producing a electromagnetic field oppose its own approach to the metal. To the electromagnetic coil, the metal is like a magnetic that increase in its magnetic field, so why doesn't Lenz's Law assert itself so the electromagnetic coil produce an Back-EMF against its own attraction to metal? Is that because the law of nature prohibit an effect from interacting from its cause? Or is that because there are subtle difference between the role and electromagnetic property between permanent magnet and ferromagnetic metal? Or is that the nature of the spring’ of the metal which can ONLY play passive role?