Is 'each other' used correctly when talking about sets of more than two people?
"We have a christian duty to serve each other. Is this statement correct**?** Because each other is used for two persons and one another for more than two persons.
This seems to be an invented "rule" that has no basis in fact.
The OED gives "each other" as synonymous with "one another" and remarks:
each other pron. used as a reciprocal pronoun (as object and in the genitive) = one another. … Some commentators on usage restrict each other to two parties and one another to more than two, but such a distinction is seldom found in actual use.
My emphasis