That is all well and good, David, but we all know what it actually means.
That does not change the fact that we shoud not disgrace ourselves
in public by incorporating error and confusion into our writing;
instead, we shoud keep it clean and strictly logical,
the same as when u bake a beautiful Angel Food cake,
u do not throw in some dirt, along with the wholesome food,
on the theory that the eater's immunity system will be able to overcome
any resultant illness.
It wouldn't matter if someone went well out of their way to suggest
that "many speakers share one right arm" for humans have enough sense
to realize that many speakers cannot share one right arm.
For the same reason that u don 't go out wearing dirty clothes, u shoud
send your written thoughts out in public, in a state of confusion
on the theory that those who see u will make allowances for u.
, in that u shoud not encourage people who see u
to have a lower opinion of u. U shoud not encourage people
to have contempt for your ability to reason.
If a person represents himself by including defects of reason
in his expression (such as saying "their right arm") then I wonder
his analytical ability has proven to be insufficient;
i.e., I lose confidence in his ability to REASON accurately.
In other words, I suspect him of being a screw up.
If someone introduces such errors of form into a resume for a job,
he puts himself into a position of competitive disadvantage,
relative to applicants who express themselves with accurate logical precision,
thereby demonstrating strength of intellect,
saying what thay MEAN, not leaving the reader to figure it out for himself,
while he laffs in derision
I KNOW, for a fact, that this has already HAPPENED
, because I was
the one laffing in derision, along with my partner, when we were reading
resumes responsive to our newspaper ads for available jobs in our law firm.
Some were very good, sharp, attractive and demanding respect,
while others were bad jokes. About 30 years ago, I was the chairman
of New York Mensa's Scholarship Committee. Again, some of the
applications for scholarship money were foolish jokes, wasted efforts,
whereas others were very attractive. I remember that I had authority
to grant 3 scholarships, but I was having a terrible time in deciding
which of the best 4 essays of application I shoud eliminate.
All 4 were so good that I coud not find one against which to discriminate.
I was looking hard for an excuse to eliminate one of them
(such as awkward self-expression).
U shoud not say "their right arm" nor say:
"It wouldn't matter if someone
[individual & singular] went well
out of their
way [plural: where did the others come from ??] to suggest"
for the same reason that u shoud not write on dirty paper and send it out with your signature.
The sentence in question does say 'the right arm of each of them"
because it can't possibly say anything else.
Most respectfully, that is a non sequitur
Even if we assume that "it can't possibly say anything else"
the possibility remains that it expresses only confusion
and says nothing at all. The literal words on the paper determine
what it says; nothing else does.
"Believe me, many native speakers would give their proverbial
right arm to have the command of English that you both possess.
'their' means each individual's right arm.
You know that it can't mean anything else.
" You know that it can't mean
anything else " is NOT
a rule of logic nor of grammar.
What u refer to when u use the word "mean" indicates
not what is on the paper, but rather the secret thoughts
in the author 's mind.
It strikes me as odd that u wish to defend and to preserve
the introduction of error into written expression.
I deem that to be very liberal and politically correct.