Rare earth metals aren't exactly rare. The most abundant of them, cerium, is more common in Earth's crust than copper and lead. All of them (with the exception of Promethium, which does not form stable isotopes) are more common than silver, mercury, gold, cadmium and even iodine.
They are, however, not found in high concentrations, and chemically they react very similar to each other, because they mostly differ in the number of electrons in the f-orbital, unlike the main group and transition group elements, which differ in the number of electrons in the s-, p- and d-orbitals (if you only know the simpler Bohr model of the electon shell: s- and p-orbital form the outer shell with the electrons most important for bonding, while the d-orbital is beneath the outer layer and the f-orbital even further beneath).
Extracting rare earth metals requires processing a much higher amount of ore, and separating them from each other requires very complex processes, which is why they are used nowhere near as much. While about 20 million tons of copper and about 5 million tons of lead are produced annually, only about 25,000 tons of cerium are produced.
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