I'm not a writer because I love to write. I don't always love writing. I avoid it sometimes. I even wash the dishes sometimes instead of writing. Some days it not only doesn't come easy, it doesn't come at all, and I have to write "I don't know what to write" over and over in my notebook just to get a few hundred words to finally trickle out.
Some days the writing does come easy. The words fly onto the page, and I look back and really like what I wrote. I love the feeling of satisfaction and accomplishment I get from a good writing session. That's still not why I'm a writer.
I am a writer because I have stories to tell. There are stories inside me all the time, some half-formed, some less clear than that. But it's constant. I am flooded with story ideas and fragments and whole stories, all the time. I need to tell them.
I think this is why most writers write, but I think it can be hard to let this be our reason. There's a lot of talk out there about your passion--living your passion, finding joy in your work (I'm sure there are hundreds of other phrases like this, but you get the idea). We think we have to be constantly on fire about our writing, in love with it, living for it.
I bought into all these ideas about finding my passion, and when I didn't love writing I thought I was wrong about being a writer. I thought I had to love writing or else I wasn't really a writer and was doing the wrong thing.