I should probably start with a disclaimer that I am writing this post mainly for my own benefit. I have serious confidence issues and letting anyone even see my writing totally awkwards me out. But I figure that if I have this issue maybe a few other writers out there do too, and we all may as well admit it, suck it up, and ask for help.
One of the reasons I think I personally have this problem is that I am afraid of people reading in to me as a person when they read my work. For example, if I write a poem about a grandfather whose addicted to tobacco (which I have) or a chubby fifteen year old who can't relate to her beautiful vice president mother but who finds solace in a job at a breeders house, helping with the dogs (which I also have) I want people to read it for what it is, and not bring me and my life in to it. First of all, sometimes its flat out wrong. (Neither of my grandfathers smoke). But the hard part is when its people who know you well reading your stuff, and you're worried they may relate the story to you. (I was a chubby fifteen year old, I completely adore dogs, and my mother is actually quite stunning.) But I am still not that character, my mother is not that mother, and I don't want people to read too much into it. I'm still me, and I don't want people's opinion of me as a person to change after they've read my writing.
Whatever the reason for the awkwardness and embarrassment at letting people see your work, it needs to stop, including for me. It can be the hardest with the people who you are closest too, but they're your base group for critique. They're who you have for support from the very beginning.
As a hopefully encouraging story, I have a really awesome professor this semester who offered to critique my work as soon as he knew I wanted to be a writer. Obviously I was ecstatic to have an English professor help me with my writing, but with that came the anxiety and awkwardness. But I knew this was an opportunity I couldn't pass up, so I sucked it up and sent him my portfolio. His response was very kind, unexpected, and helpful. His favorite piece was one of my least favorites, and he didn't even really address what I thought he would like the most. But he gave very insightful reasons about why he liked what he liked, about my strengths and about how I could use those strengths to improve my weaknesses. His advice has really helped me.
So don't stress about letting people read your work. They will still love you, you will be the same person you were before they read it, and you may get some great help from them, or at least some support. So suck it up and find someone to be your best reader.