rare earth because there's only one earth duhhhh

;-)

They are “rare” in the sense that they are never found in high concentrations, and yeah you have to process a lot of shit you dont want out in order to get them isolated. Other than that they are literally everywhere, just in tiny bits

Because they behave similarly electrically, chemically and dynamically by mass. So all the various ways of processing materials then always have a difficult path to separating the elements that are close to one another. Plus they're actually rare so only found in high enough concentration to make any economical sense getting from specific areas until there's a big enough market.