I love this question. I used to think there was something big I needed to do to earn the title of "writer," like I had to earn it. Write a book. Get something published in a swanky magazine everyone's heard of. Start a "successful" blog -- though my definition of success kept moving further and further away even as I took steps towards it.
Looking back on my life -- as someone who had really poor self-esteem, then, recently, blooming into someone who loves her life and feels worthy of good things -- it makes sense that I couldn't claim "writer" as my own when I felt so low.
Now, I OWN IT. I've practiced telling people that I'm a writer when I introduce myself -- which was really hard at first! But there was some growth that happened even in that small gesture, some confidence gained. Which gave me impetus to press "publish" a little more freely. Which caused people to see my writing a little more.
The pattern continued to the point when, now, my friends refer to me as their "writer" friend. Which is so cool and fun and I don't feel imposter-syndrome-y about it all! I feel, rather, that I LIVE that life, so I may as well own it.
If I had to boil it down, my reason for freely calling myself a writer is because I write things. I think that's all it takes. I love celebrating all my fantastic "writer" friends, finding their way, even if the only thing they write is fantastic Facebook posts. I honor their journey, and their creations.