When a interviewer asks you a question like this, then the meaning behind this question is:
The interviewer may be indicating that you have failed to convince them so far that you are the best candidate for the job. Alternatively, they may just be asking you to pitch yourself. What they’re really looking for is for you to give them at least one good reason why they should be hiring you and not someone else.
So, there can be 3 approaches for this question:
You should hire me because I am the best person for the job. I realize that there are likely other candidates who also have the ability to do this job. Yet I bring an additional quality that makes me the best person for this job and that is my passion for excellence. I am passionately committed to producing truly world class results. Then you could give an example.
Your answers should be brief but relevant to your qualifications and experience related to the job you are applying for. Talk about your education, internship experience and skills. Keep the topics and subject matter business related and professional at all times.
Also, try and focus on what you can do for the firm, the practice group or the individual. If you are interviewing with a top firm and are aware of their reputation, let them know. It is a privilege to work for the top firms. Getting into the best firms requires knowledge of why these firms are so special.
Your answers should be focused on your strengths and proven track record of a job well done.
I couldn’t comment on other candidates for the job but I can say that, I have been working in this industry for over a decade, I have built up a very enviable network of contacts which I think most other candidates would find hard to beat. I have developed successful relationships with key decision makers in numerous companies and this enables me to achieve a sales conversion rate much higher than average. I believe that my previous track record is clear evidence of what I would be able to achieve for you if you decide to appoint me to the role. I’m ambitious, highly driven and I relish a challenge.
You don't have to grovel on a job interview, ever. You don't have to be evasive. You can say flat out, "I don't know that you should hire me - there may be someone in your interview roster who's a better fit for the job."
You can tell the truth, politely and forthrightly, on a job interview. Using your alternative answer to a job interview question that should have been retired long ago is one way to start reclaiming your power.
Let me give you a small conversation example between a (Hiring) Manager and a Job Seeker
Manager: Let me ask you - with so many talented people on the job market, why should we hire you?
Job Seeker: That's a great question. I'm glad you brought it up. That is a big decision that you are going to make, and my take is that I don't envy you for the decision process, and I'm not sure you should hire me.
Manager: Why not?
Job Seeker: You know the company, and you know the role. You know yourself and your management style. I know me, but you know almost everything about what's needed here given what you're facing in the marketplace. And most importantly, you've met all the candidates for the job. I've met only me. So I don't know that you should hire me, but I know one thing.
Manager: What's that?
Job Seeker: I know that when I find the job that is right for me and vice versa, I'll know it, and my hiring manager will know it, and everything will work out just the way it should. That could be this job, or it could be a different one. I have total confidence in me.