While our literature professors may have embedded this idea in our heads since middle school, the relationship between reading and writing is not as straightforward as it may seem. Yes, they are obviously closely related. But, it does not mean your interaction with one will affect your skill in the other.
As someone who has written for several organizations, newspapers and magazines for a fair amount of time and can barely get through half a book, I never understood the basis of this concept. And so, trying to decipher it was like a roller coaster ride.