I have been writing for a long time—professionally for the past several years. I still suffer from No-one-will-ever-appreciate-me Syndrome. This disease (that every writer feels occasionally, good writers bi-weekly) is caused by...well, I don't know. I'm a depressed writer, not an depressed psychiatrist.
Whatever the cause, low confidence is something we deal with; and it's something we constantly overcome. I say overcome, but I should actually say sidle up to for companionship. Sometimes we will take comfort in our own pitiful self-disrespect. Yet somehow, it doesn't hinder us in our work, it just makes us weird people.
What I want to address is not how to get over low self-esteem, but how to let our work speak for itself, and how accept criticism without taking it personally. The work is what drives us, it's the work that should carry us through.
If people enjoy our stories and poems, then we should let them praise them without puffing ourselves up. Puffing up is a sure route to stagnation. On the other hand, if they hate it, we should let them. They don't hate us (well some of them do but that's not important here). Sometimes they hate it because it's bad, and that's okay. Wouldn't you rather know that it's bad, so you can move on to write something good?
We must focus on our purpose in writing. I write not only because I enjoy it, but because I feel driven with a spiritual compulsion. That may sound extreme; and so it is. Writing is something that can change the world, and I want a piece of the pie. Sometimes I feel like a protestor throwing rocks at a tank, but one day my rock is going to hit the tank in the right spot and it's going to explode. Compared to the World Tank, my rock isn't much, but it has weight. It has purpose. I believe in my rock.
We all have different motivations when we write. One person tells funny stories for her kids, and someone else writes opinion pieces for the Wall Street Journal. Unfortunately, you may come to the same realization that I come to quite often: that the things you write have very little impact on the world. I want to tell you that this realization is a lie.
You believe in your writing, and it can change the world. It may not be a rock thrown at a tank; it may be a flower thrown on a stage. It can change one person's world. So, when people read your writing to offer praise or criticism, listen. Let their words improve your work because it's the work that matters.