“Why should we hire you?” is not actually about you

Most people answer this by summarising their résumé.
But the interviewer already has your résumé.
What they really need to know is:
What problem can you solve?
Where have you proved it?
What makes you different?
Why do you actually want this job?
The strongest answer isn’t “I’m hardworking and passionate.”
It’s specific, believable, and makes the hiring decision easier.
How do you answer this question without sounding rehearsed?