Whenever I discuss pride in writing, people almost immediately think of pride in a negative way. They assume that someone who is proud of their own work is some kind of a pompous jerk. They equate a writer citing one of his favorite stories or his best writing accomplishments with a rich New York socialite looking at herself in the mirror and smiling. The flip side of this is a writer taking no pride in writing and referring to himself as a hack or somehow inferior to the best writers of his day. This latter side is how most people think in general, referring to themselves in a negative way and saying that they could never be as good as "him" or "her."
When I finish a day of writing, I certainly feel a sense of pride and I'm happy to share it with others. When I've created something that I'm proud of, I'd much rather feel a sense of accomplishment and express it with people than to try to keep up some kind of facade. First of all, it feels so much better to say the words, "I am a writer," than it does to water it down. When you don't have a lot of pride in writing that you do, you are likely to say something like, "I work at a coffee shop and I do some writing," or "I'm a temp and I write on the side." You may be creating a self-fulfilling prophecy by placing writing second, third or anywhere other than first in that sentence. If you want to be a writer, you should say that you're a writer. It will probably make your writing stronger and more confident.
Secondly, writing is so tough sometimes that it's important to be supportive of yourself. When you are your toughest critic and you assume that nothing you write will ever be good enough, whether or not you're right, you are keeping yourself from doing something that you love. You are trying to discourage yourself from writing. Take some pride in writing. Be proud of the fact that you've produced something. And if you haven't yet, then go and write something and then be proud of it. I'm sure there are plenty of great writers who beat themselves up about a sentence they could have made better here and a character they could have made more well rounded there. Personally, I'd rather not live that way. I've had scripts and stories I've written torn into shreds by critics. I've had them torn into shreds mentally by myself. I refuse to be swayed by their opinions or my own. I know that I want to be a writer and I'm going to write, negativity be damned!
Lastly, pride in writing will also help you to promote your work. If you're worried that someone might think your writing isn't good enough, you might not do as much as you need to do to get people to buy the dang thing. Be excited and be proud of what you've done, and you'll already be miles ahead of those who are more talented and too fearful to write a single word.