My answer to that is: well, depends what you mean by write.
If writing is stringing words together in a way that it summons an image in a readers head? Yes, you can learn to do that. If it means plotting, and the sweep of story, and how the characters evolve? Then yes, you can learn how to put a plot together, you can learn how to make realistic characters. You can learn how to come up with ideas, to extrapolate those ideas until you have a plan, and then you can learn how to put words on it.
But in my mind, there is one thing you cannot learn. And that is how to get the characters to talk to you, how to get your books unfolding in your head. You can learn all the separate elements of this, you can learn how to twist plots, how to formulate characters, how to write well. But you can not learn how to put those together. You can learn how to put them together better than you already do. But there has to be a certain level of "story cohesiveness" that is acquired by instinct.
My reasoning for this is simple. A story is made up of so many different elements. Truely, there are more than I can think about and know of. To learn how to perform all of these elements and then to try and figure out a way to tie them all together using a plan or a method - it would make your brain explode, truly it would.
Imagine a musician. You can learn how to hold an instrument, you can learn how to make sound, you can press keys, make notes, perform music on a sheet of paper. But when it comes to creating something of your own, you either manage to create art, or just sound out notes.
I beleive that anyone can learn the tools and value of writing. But you must intrinsicly have storytelling in your being. Now, if you're a plotter, with every point and character twist plotted out, this is not writing by numbers. It simply means your first draft is in a form that is different to my first draft. If you have to figure out characters before you start, then this is not what I'm talking about.
regardless of the amount of information you have to have before you can start a story, regardless of how hard it is to put a story on paper, regardless of how many times you fail - this storytelling ability is there. You know you have it the moment you put it on paper.
Because you are writing. You are writing and characters, or plot, or your outline just speaks to you. there is no proper way to describe it. It just happens. Maybe only for a chapter. Maybe the rest of it is a terrible slog through nothing. But for a couple of brief moments, you feel as if the thing is alive.
This doesn't mean that your characters are running away from you and making their own decisions. I know plotters who have never had that happen to them. But their ideas are alive for them, the way they think about things are alive for them. For discovery writers, things have to be alive from the get go, otherwise you're never going to progress to the next chapter.
If you want to prove me wrong, if you have the need to write, although you haven't had things come alive for you - well, chances are it's already happened, maybe only for a brief moment, and you missed it. Because I can't think of any other reason why someone would put themselves through the agony of writing a story.