Well, I have to say that that is not a particularly true statement, and there is nothing special about writers in this regard. Just like with anything life, the debate isn't that simplistic and it happens in many different areas.
I don't understand the "nobody else is expected to work for free" argument to begin with. The expectation of free work is found in all kinds of fields. The position of "unpaid intern" can be found just about anywhere, and you don't hear people screeching about them. Individuals choose to work for free all the time as a way to drum up new clients, to build some good-will or to establish some new word-of-mouth connections. This is certainly not some writers-only thing.
So why would you ever take a writing job that doesn't pay? Just like in these other fields, there are many good reasons. It can provide some experience and let some others read your work. You probably won't get any really hard-core editorial commentary from someone who isn't paying for your work, but you can still learn from a little feedback. Even with some small-potatoes website job, you can still gain a little exposure for your work and it creates a place where you can point people who want to see some published clips.
Sometimes the simple fact that your writing has gotten accepted by someone can be a huge boost to your personal morale.
A new website may brag about giving you a ton of exposure. You should take that with a grain of salt. Some site with no money to pay you probably isn't about to take the world by storm and bring your words to millions of readers. Just something to consider on that front.
You may also luck out in getting future paid work once your foot is in the door with a freebie gig. Not always, but it does happen.
None of these reasons is going to appeal to a long-term professional who can normally pull in $50/hour pay rates. For a novice with few other prospects, it can be better than nothing.
Personally, I take in opportunities at varying levels, including some for free because I enjoy the topics and some where I expect higher pay because I know the client has the money to warrant it. I've also won myself decent jobs because I had a nice application proposal that was well done and on topic. The prospective client had no idea that the earlier work had been done for free, and it really didn't matter.
Many people are unreasonable in their expectations about getting writing done for free, or for pennies per hour. I'm not saying this isn't a real problem. The number of times I've seen people willing to pay no more than $2 for an article makes me want to scream. But to imply that writing for free is completely out of place is also untrue. There is a time and place for everything, including writing for free.