Is the semicolon in the following sentence misused?
How can I miss you; we've never met?
I feel that the sentence, to be grammatically correct, must be split into its individual parts.
Yes, that's wrong. A semicolon is supposed to connect two related clauses. What you have there is a question and a statement, with a semicolon for the question and the question mark on the statement.
Something like "I can't miss you; we've never met." would be proper use of the semicolon.
Or, "How can I miss you? We've never met." would be proper punctuation for the given sentence.
Or, "How can I miss you if we've never met?" would be a proper replacement for the errant semicolon.
I do not believe this is acceptable. The sentence should be rewritten several ways, but not the way you have cited.
1) How could I miss you? We have never met. // Fine.
2) How could I miss you, as we have never met? // Okay.
3) As we have never met, how could I miss you? // Perfect.
No matter what, "how can I miss you" is its own interrogative statement. It requires the use of the question mark. Breaking the sentence up with the semicolon puts the question mark near the end, where the question isn't.
Hellion's and Evik's answers are already very good, but should you have any more doubts on this topic in the future, you might want to refer to The Oatmeal's Guide on “How to use a semicolon - The most feared punctuation on earth”.
Evik, changing the order changes the meaning, so that's a judgement call as to whether it's better. It depends on the text as a whole. What I would do, though, if I were to change the order, is leave the semi-colon.
"We've never met; how could I miss you?"
This is a classic context for the colon: the second half amplifies or explains the first.
Evik's "As we have never met, how could I miss you?" and Hellion's "How can I miss you if we've never met?" are certainly more correct, but they convey a very different feeling. The problem with "How can I miss you; we've never met?" is more with the question mark, I think.
None of the variants I have seen or tried myself did convey the same meaning and feeling, though, so if I was the authors, if the context allow, I would probably keep it unchanged, even if not perfectly grammatical.