If you want to tell stories, you have to get a sense of how they work and how certain choices affect the audience engaging with them.
Reading other works gives writers an invaluable look at how others put stories together and how we're affected by them. It's grounding.
It's also hard to build that experience, that innate sense of storytelling, any other way. Part of learning how to tell stories is engaging with stories themselves.
I wouldn't go so far to say you can't be a writer without reading, but I do think you miss a lot if you don't.