"That person is our doctor."
why is it wrong not to add the second word in this sentence since you can say "that" without it?
If you are referring to the "ge", I think in Chinese you must have that word when you refer to a person. I believe it is a required "measure" word, like "a" or "an" in English, though in this case we wouldn't use those words in English.
Isn't it rude to use the measure word ``ge'' for people? Wouldn't wei 位 be more polite?
Although "位" is more polite, "个" is usually not considered rude. However, "个" cannot replace "位" in common phrases like "诸位".
I believe it is wrong because the English sentence clearly states "That PERSON..." I think since you eliminated it in your response, what you really said in English is "That is our..." rather than "that PERSON is our..."