Not all readers are going to be great writers. Some aren't going to be willing to put in the time and effort to sufficiently not suck at it, while others just aren't interested.
But if the creators of crappy writers' memes are to be believed, every writer worth their salt is, almost by definition, an avid reader.
When you write enough, reading isn't the same as it once was. A writer's relationship with books can be different than a layperson's. When you know how the sausage is made...
1. Reading starts to feel like work.
One of the reasons it's so important for writers to read a lot is that every book you read is research in the craft. You're constantly analyzing the authors' styles and methods, guessing at their motives behind word choices, etc...
That thing you used to do for pleasure, now it feels like work. Reading a book can be a chore when you're picking it apart and mining its author's secrets.
2. You start to see through writer's tricks.
A magician never reveals his secrets. If he did, the magic would be gone. If the audience can see the contortionist all squished up in one side of the box, and the pair of prosthetic legs on the other side, they're literally just watching a man saw an ordinary box in half.
The audience knows going in that the man on the stage with the sequined suit isn't actually conjuring the Dark Arts to choose the correct playing card. They're paying to be convincingly lied to.
The contract is similar for writers and readers of fiction. Writers are paid to convince readers, to the best of their abilities, to believe a story about shit that never happened. And we use tricks. And when a writer is reading, some of those tricks can be recognizable, and telegraph upcoming events which were meant to be a surprise.
If Princess Penelope picks up her fork during the dinner scene, a casual reader might not think anything of it. But we writers know that Archduke Fontebleau is about to get stabbed in his fucking eye. And then we conclude that she isn't really the princess at all... She's actually Count Sumpterfump's long lost daughter.
How do we know? Because the fork was mentioned. There was no reason to mention Princess Penelope picking up the fork. It's a dinner scene. The reader can be trusted to assume that the people in the scene are using utensils.
Now when Princess P. shouts "FORK YOU!" while blood gushes out of the Archduke's ocular cavity, the writer-reader yawns smugly to himself.
3. You notice flaws.
What if you finish the whole dinner scene and nobody gets stabbed? The princess and the archduke hit it off pretty nicely and their eyes meet when they inadvertently start to eat from opposite ends of the same noodle.
While the hearts of non-writer-readers are warmed at the romance unfolding before them, the writer-reader is still seething about the fork.
"What the fuck? Why did he mention the goddamn fork? Nobody else's fucking fork got mentioned. Should I take that to mean the rest of them were eating out of troughs?"
Here's a real world example. My wife suggested we watch "The Intern" a few weeks ago. After I took a look at the trailer, I had an idea of what to expect.
Robert De Niro plays an old guy who interns for a no-nonsense whippersnapper boss. They don't get along at first, seeing situations from two vastly different perspectives, but slowly they come to realize that there is value in the other's perspective, and they come to be friends or some shit.
And that sort of happens... in the first twenty minutes. Anne Hathaway's boss character gets weirded out by a too-good-to-be-true De Niro, and orders him to be transferred somewhere else. Then, the very next day, she just thinks 'What the fuck have I done?', and has him transferred right back.
There goes what I assumed was going to be the central conflict of the movie. So what is the central conflict?
NOTHING! Robert De Niro's character is a perfect human being. No flaws. No problems. Nothing. This is literally a movie about Rober De Niro being old and adorable for two hours.
His boss has a hiccup of doubt about him in the beginning, and then gets over it. The scruffy youngsters at the company idolize him. The company masseuse (because that's a thing in this movie) practically dry humps him in front of the staff until his 70-year-old dick pitches a tent in his suit pants.
About eighty-five percent of the way into the movie, there looks like there might be a spot of conflict happening after all. The perfect old intern catches his boss's husband with another woman. Pretty late to introduce a conflict, but I'll take what I can get.
Will he tell? Won't he tell? Of course, he doesn't get a chance to, because she already knows, and tells him so.
So why am I spending the lion's share of this post reviewing a forgettable comedy from last year? Because the storyteller in me was so bothered by sitting through two hours of a story with no conflict that, as forgettable as it was, I'm unable to forget about it.
4. You come to realize just how much you suck as a writer.
Sometimes none of those first three entries apply. You read a book, or see a show or a movie, and it blows you away. The prose paints vivid images in your mind. The dialogue sings. You're surprised, you laugh, you cry. You get so engrossed in the story that you suddenly remember that you were supposed to pick up your kids from school three hours ago.
Then it hits you. This is what real storytelling is. How dare I expect people to pay me money for the horseshit I'm writing?
With all the great literature in the world that no one can read in a single lifetime, is it not a crime against humanity to peddle my own septic garbage?
Are my stories, and by extension my very existence, a blight on humanity?
Each of us must answer these questions for ourselves. For me, the answer is clear. With the alternative being me having to continue working a "real" job, humanity can suck it.