Everyone can write, if they triy, but that doesn’t necessarily mean it’s going to be good, something that others will enjoy reading. There are plenty of ways to improve, from daily writing and using prompts to listening to constructive criticism and being willing to edit.
I firmly stand behind the idea that one needs to read in order to write well and I’m not just talking “How To” books, although those are helpful too. I can’t tell you how many pieces of writing I’ve seen in crit groups that don’t have proper dialog, thought or flashback formatting, that have stilted dialog with outdated or too old for the character vocabulary, that don’t know how to keep the plot flowing or how to build the tension to the climax.
Reading books in the genre in which you write can be helpful to teach you how to handle formatting and how to better build a world or well rounded characters. Not only will reading help your writing, but it will show you what’s trending in your genre at the moment and the kinds of topics publishers are picking up (although that’s not to say you need to follow the trend because by the time you publish, the trend could have changed.)
I’d have to say I’m not sure I’d trust someone who claimed to be a writer and then told me they don’t read. To me that would signify that the person was more a hobbyist who writes for fun but isn’t really looking to improve upon themselves to hone their craft. There’s nothing wrong with that if they’re just writing for enjoyment, but if they’re looking to publish, gently point them in the direction of your local library and tell them to get readin’!
Do you think reading is an important aspect to writing? Why or why not?