Anyone doing any kind of work should be paid (writing, drawing, editing etc).
What that payment should be can get VERY complicated, so to keep it simple, the people involved in a project need to sit down together, reveal their demands and expectations and hopefully come to an agreement.
Why this debate about writers keeps popping up is due to a situation that is the reality of indie comics. A lot of people want to tell (write) stories, but statistically speaking far fewer people can/want to draw. Also, coming up with a story and writing it (not necessarily a good one) takes less time than drawing the story (not everyone is willing to accept this, but from my writer's point of view, it's the truth).
That is why writers, even in the mainstream media, usually work on more than one project at a time, (I heard of writers working on 3 different titles) but artists can only work on one title at a time and keep up with the deadline. If you check the standard page rates, you will see a writer is paid less per page than an artist, which makes sense to me personally.
For this simple reason, you have an influx of writers wanting to create comics and tell stories and never enough artists to meet the demand (even if you did, the are people always willing to pay to get work done, as it should be in an ideal world). Therefore when the project is NOT a collaboration where they both agree to work for free and hopefully make some money when they are done with the project, it is usually the writer that funds a project by hiring an artist to work for them (remember, way more willing writers than artists out there, regardless of skill). That is the majority of all indie comics, and so in those cases, the writer pays the artist to draw for them, and the writer is not paid anything. If they do a good job then maybe they will make some money when/if they sell their comic.
This has created the idea that writers should not get paid. Especially if you are an artist and decide you want to draw a comic, just post that you are looking for a writer to collaborate with and be willing to work for free on the project, and you will be flooded with messages from writers (not necessarily good writers, but that isn't the point).
So the idea is, writers should not be paid when making indie/free comics. Artists need to get paid because if you want the comic on a deadline then drawing has to be their full-time job. However, as a writer, you can also have a full-time job and earn a living from something else while writing stories (this has been the case for me personally, I had a full time job other than writing stories). That is the main reason, I believe, why some people might say that writers should not be paid when the same people will say that artists should always be paid (and I find myself agreeing with the paying the artist part).
But these kinds of conversations always assume that the writer is the one trying to start this project and should therefore pay. The same way a mainstream company pays ALL the creators, including writers, working on their projects. I believe the conversation you saw, that states writers should not be paid is about a situation similar to the indie comics I am describing here.