In a writers' forum I participate, the question has come up of whether writers really need to read. The answer is yes. I'm not one of those who say that a writer needs to read fiction in their genre every day. You probably should read plenty of fiction in your genre, but I'll admit that I go through dry spells. Sometimes I'm reading a book a week, and sometimes I may go months between reading books and even stories. However, even given the occasional dry spell, I have amassed quite a catalog of books in my genre that I have read. So even when a writer isn't reading a lot now, I would hope that he's read a lot in his formative years.
I sometimes think that I don't read widely enough, or read enough. But even when I'm reading the least, I easily read ten times as much as I write. So it's hard for me to comprehend how writers could hardly read at all.
Why is reading so important? If you read a lot, won't your work sound just like everyone else's? Well, yes and no. Part of the reason to read a lot is so that you absorb the elements of writing. At the most basic level, that's vocabulary and grammar, and how to put together coherent sentences and paragraphs. How to describe a scene or an action. Believe it or not, a lot of would-be writers have never learned, or at least are very rusty, with these basic skills. They may have learned them in grade school, but a lot of people haven't practiced them since, and seeing how to use the language helps immensely. Beyond that, there's plotting and pacing. Mood and characterization. I don't think anybody knows how to do these things without seeing how its done by others. In our day to day lives, we communicate verbally. And while verbal storytelling has its place, it's not the same thing as the written word. Nor is video, such as televisions and movies. The techniques used in those forms are not the same as the ones that a writer can effectively use.
I shouldn't minimize the danger of homogenization, where you start to sound like exactly what you read. It happens (though I think that creative writing classes are more homogenizing than reading). The cure to that is to read widely. Read recent stories and old. Read different genres. Read fiction and non-fiction. Read books written in other languages (in those languages, if you can).