Nathan Bransford has a post up called Writing as an Identity in which he argues that writers shouldn't be wrapping up their identity, their sense of self, in being a writer. When writers begin to identify themselves as writers, when they treat it as something more than just fun, they "begin to wrap up their identity with the publication process, the rejections become personal, and a judgment on a book becomes intertwined, in the writer's eye, with a judgment of self."
Now, he's probably right about people taking rejection too personally. However, nowhere in his post does he mention that people in other fields identify with their work. In skimming the 432 comments to his post, I didn't see anyone else bringing it up, either.
They may have been totally focused on writers being some kind of special artist different from the rest of the world. But we're not. We're like many other people in many other fields of work who get a sense of identity from what they do every day of their lives. That's not a bad thing. If anything, it's a good thing.
I'm not talking about workaholics who wreck other aspects of their lives. That's not the same thing at all. I'm talking about people who live their lives with a certain sense of purpose or live their lives in a particular way because they are engineers, nurses, or teachers, to name the professions I'm most familiar with in my personal life. They think a certain way and respond to situations in a certain way because of their training and the way they've spent so much of their work lives.
I think people are lucky if they're in a line of work that fits their psyche so well that they identify with it and are engineers or health care professionals or teachers or...writers.