My rationale for this is that asking yourself questions is a good way of reflecting on what you know and what you think you know and how you think. It doesn't matter whether you know the answer to the questions you're asking, but just observing yourself try to answer the question gives you a better idea of who you are, what your values are, and why you think they way you do. I do this a lot to gain better understanding of myself and see whether I'm liking the way I'm thinking or whether I can still improve my thought process and eventually be able to change the way I think.
You might ask why would I even want to know the way I think -- and I think that's a valid question. Personally I find that since learning more about the way my thought process works I've been able to synthesize better questions, better answers, and better ideas in general. It allows me to see what approach I'm taking and be able to decide whether I want to change that approach and see things from a different perspective. I also find that the more I do this the more I understand how to control what I say, what I do, how I react to situations, and whether I'm happy with the approaches I've taken so far.
Reflection and introspection are important I think for you to be able to better quantify and identify what your current state of being is and help you decide on whether you'd like to improve your strengths, address some weaknesses (you first need to be able to identify them), and be honest with yourself. Ever since I've identified a long time ago that drawing was something I am not strong at, I now feel less frustrated when I try to draw anything -- I acknowledge my deficiencies and at some point I can decide to improve on this if I want to. Doing similar exercises has allowed me to prioritize which parts of my life I would like to work on, focus more on, and be able to actually address.
Of course you can enjoy reflection and introspection even if you don't plan on changing anything about yourself. It may be a personality trait (or character defect) of mine that makes me want to optimize every aspect of my life -- along with a lot of other geeks I know -- which makes me want to keep improving myself according to my standards, but I know people who are content with who they are and get more content the more they know about themselves. Some people don't have a mission of self-improvement but have a different mission in life and they know it -- for the most part, knowing yourself and what your mission is definitely helps in gaining better peace of mind and focus to do the things you want to do.
For a while I've been meaning to get my hands on Zen books especially since I read Zen and the Art of Motorcycle Maintenance. If you haven't read that book yet I highly recommend that you do so. I think I can relate to the main character not because I'm feeling schizophrenic but mostly because the path of (re)discovery especially of yourself is one of those paths that only you can take. Looking inside yourself (introspection) as well as at yourself (reflection) is that one thing you are able to do that nobody else can do for you. There's a very comforting and (potentially) addictive aspect to this that's the stuff of countless books on the topic -- for me it's just really refreshing to get to know myself better especially inspecting the way I think.
If you haven't done this yourself, give it a try. I would definitely love to hear about what you think about doing reflection and introspection. I believe it's inspiring hearing or reading about people's thought processes and how their self discovery has improved their lives for the better.