Breakdown of Hvorugur þeirra er læknirinn.
vera
to be
læknirinn
the doctor
þeir
they (m)
hvorugur
neither of two
Questions & Answers about Hvorugur þeirra er læknirinn.
How does "hvorugur" relate to the "hvor" vs "hver" rule we're learning?
Hvorugur means "neither of the two". It is built from hvor (which of two). If you were talking about "none" of a group of three or more, you would use enginn instead, which is the negative equivalent for larger groups.
Why does the verb "er" (is) stay singular when we are talking about "them"?
Even though þeirra means "of them", the main subject of the sentence is hvorugur (neither one). Just like in strict English grammar ("neither one is"), Icelandic uses the singular verb er to match the singular subject.
Why is it "hvorugur" (masculine) and not another gender?
It matches the gender of the group being talked about. Because the sentence uses the masculine hvorugur, we know the speaker is talking about two men. If it were two women, it would be hvorug þeirra (feminine), and for a mixed group, it would be hvorugt þeirra (neuter).