Why is their in the following sentence wrong?
The modern American family differs in many significant ways from their nineteenth-century counterpart.
Why is their in the following sentence wrong?
The modern American family differs in many significant ways from their nineteenth-century counterpart.
It's wrong because family is singular and their should be used for plurals (apart from singular their, which can't be the case here).
For singular you use its, therefore:
The modern American family differs in many significant ways from its nineteenth-century counterpart.
Or you make the subject plural, thus having:
Modern American families differ in many significant ways from their nineteenth-century counterparts.
OP's sentence is wrong for most Americans because they normally, esp. in recent decades, treat "the family" as singular, so they would expect "its counterpart", not "their counterpart".
It's wrong for Brits because although it's true we often treat "the family" as plural, if we did that in this particular case we'd obviously expect "The ... family differ", not "differs".
But it's worth pointing out that Brits don't always treat these "group nouns" (family, Parliament, the government, company names, etc.) as plural. In this specific case I think most of us would use the singular anyway, because the family is referenced as a single entity being compared to another single entity (its "collective" counterpart).
It's also worth pointing out that I doubt many native speakers would be happy with...
?*The family took its places at the table.
...which just goes to show that there's no single "logical" approach anyway. I put that example up because you can fix it using singular "they", or simply by saying "the family" is plural anyway (in which case you can legitimately use "plural 'they'"). But if you insist "the family" is singular, and you don't endorse "singular 'they'", you're stuck with the very ungainly form above!
It's not wrong, but I would have worded it like so:
The modern American family differs ... from its nineteenth-century counterpart.
Here everything is singular: family / differs / its / counterpart.
If you substitute the singular they in that sentence, it's equally valid and becomes what you had originally written:
The modern American family differs ... from their nineteenth-century counterpart.
Another way to word it is to make everything plural:
Modern American families differ ... from their nineteenth-century counterparts.
From what I understand, 'their' is also a sign of ownership. From what I further understand, it is part of what you're implying when you say it is THEIR counterpart.
The modern American family differs in many significant ways from their nineteenth-century counterpart.
If we were to completely take away the middle part, we'd get this...
The modern American family differs from their nineteenth-century counterpart.
Now, you can use 'its', but while it is still an unresolved issue with ALL of the English language, it is one of those accepted things. Singular 'they' does exist and it CAN BE used here. (My earlier argument, for this case just is another piece of evidence for the pro-singular 'they'.)
I'd further like to say that you have listed the noun, it is not nondescript. You refer to a family as a person or as (a) people. That is another reason why 'their' is correct. 'Family', in this case, is being viewed as people, as in plural. (And this last bit was for everyone who thought the sentence was wrong.)
Case closed.
Using their in that sentence is not wrong. It is right for either of two different paths:
It is right if you construe family to be a plural, as such things frequently are, especially in British English.
It is right if you construct their as here referring to a non-specific or non-sexed singular antecedent.
Either way, the usage is correct.
Of course, correctness has never stopped people from complaining about things; people will always complain.
It's wrong because their is plural and counterpart, to which their belongs, is singular. That simple. Whether family is singular, plural or both, and whether they can be singular if paired with a non-specific referent (both fruitful sources of disagreement, obviously) have no bearing on the case.