Open-ended interview questions from hiring managers are great ways to solicit information from job applicants. What's lousy about the open-ended questions, however, is when they are simply open-ended and not open-ended about the job.
As a result, "Why should I hire you?" is a dangerous interview question. You have no context with which to orient your answer to what the hiring manager is looking for in the position. So your answer can be spot-on or wildly off base. Just what you want in an interview...
Start with your value to work; your personal brand
While each of us have done work that qualify as a "position" -- let's say a nurse -- each of us also brings particular skills to the job that differentiate us among nurses.
For example, my tag line is "rubber meets cloud." I'm good at implementation of projects. I can see the high level of work and gateways and management intentions while being perfectly capable of getting into the weeds of the tasks with anyone to get the work done. That's one of my special job skills that I bring to project management.
Or, my special skill as a manager is that I figure out how to get the best work out of each individual on my team. I have various ways of doing that, but I have a track record of getting teams working well together to get stuff done.
You have that same unique set of skills for the work you do as well. It might be delivery, creativity, focus, problem solving, process fixing or a hundred other things.
Use your personal brand to show value to the job description
When you get asked an open-ended question about you rather than the job, the only criteria about the job you can fall back on is the job description.
Consequently, before the job interview, you need to have already decided what value you bring to the major portions of the job description. You start with your personal brand values and then go through the job description and apply the values to the job.
If the job description reads that the person needs to work in a fast-paced environment and one of your unique skills is your ability to quickly reorient your focus, you can build part of an answer to a "why should I hire you?" question based on the fact that you quickly change focus as the daily pace changes while still achieving your goals.
Having 2-3 of these "unique performance values" related to the "job description" will give you the cleanest way of beginning to answer the "why should I hire you?" question.
Why should I hire you?