According to this answer about quoting a question in the middle of a sentence, the punctuation in this example sentence is correct:
People are not merely asking, "why should I do this?" they're asking, "why should anyone do this?"
But not only does it look like two separate sentences to me, maybe it should be:
People are not merely asking, "why should I do this?" They're asking, "why should anyone do this?"
If it's made into two sentences, then I'm not sure the second one is complete enough, or supported enough by the context of the first sentence, to stand on it's own.
Are they both grammatical? If so, are the two examples equivelent? Do they take on different nuances?
Best Answer
I think the rules can shift a bit depending on the style guide you're working from, but most would probably require:
Since the last rule would strip away both a comma and a period after the first quotation, the only way to draw a distinction between the example being one sentence or two is the capitalization of the word "[T/t]hey're," and each choice is grammatical. The main difference is the length of the mental pause placed when parsing the line, which may augment or diminish the rhetorical effect of the antithesis. The effect will vary from reader to reader, and many people may interpret them as being identical. Some people may also find one version easier to parse on the first attempt, but this again will vary from person to person (I personally find the two-sentence version easier to parse, but I see in the comments that Jim made the opposite observation).