This is one of the many ways the feelings of not being good enough or of unworthiness show up in your life and get in the way of your success, fulfillment and authenticity. Sadly, as most of people know, this question doesn't come from your true self; it comes from your "Gremlin," the little monster in your head whose only job is to keep you out of perceived danger. The more you listen to your Gremlin, the more you allow him or her to sabotage your life.
However, this question, "Who do you think you are?"—while often asked in a negative, critical way and is something you allow to stop you from doing, saying and going for important things in life—is also a very important question for you to ask and answer honestly. When you look at it on deeper level, you see that your answer to this question has a lot to do with how you experience life in general.
How life is for you has a lot less to do with your circumstances or situations and much more to do with how you relate to them and the thoughts you have. Some of the most powerful thoughts you think and the ones that have the most impact on you are the thoughts you have about yourself (i.e., who you think you are).
Everyone has a story about themselves and their lives. These stories are often dramatic, funny, scary, inspiring, sad, intense, boring, enjoyable or tragic (usually a combination of many of these things). In most cases, the story you have changes a bit, depending on how you're feeling about life and yourself at any given time.
One of the things you may sometimes forget, however, is that you're the author of the story of your life, not just the main character. You may think that your story has to do with all the things that have happened to you, the qualities you were born with or have cultivated, the stuff you've done or haven't done yet. But, when you remember that your story is a function of your thoughts, most specifically the thoughts you have about yourself, you can be empowered to consciously transform not just your story, but your life as a whole.