A writer writes, for the same reason that a dancer dances. Just as a dancer's feet glide across the floor, so do writer's fingers glide across the keyboard. As dancer's arms flow freely, a writer's thoughts flow equally so. Both find joy and maybe a sense of freedom, from his/her independent movements (thoughts) and both realm in the sovereignty his/her talent brings them.
A writer writes, for the same reason that a builder builds. Just as a builder assembles his/her work, so does a writer. The materials used to develop are different (a writer uses his/her ideas) but each strive to create strong structures, with solid foundations. Each has their own set of blueprints; each has their own level of integrity and degree of expansion but both share equal goals of completion.
A writer writes, for the same reason that a singer sings. Just as a singer has the capacity to hit high musical notes, a writer has the same aptitude of achievement. The act of singing fills the singer with emotion, whether it is of a happy or of a sad nature. The same holds true for a writer. However, while the singer expresses his/her passion vocally, a writer's musical notes are in print.
A writer writes for the same reason that a painter paints. Just as the strokes of a painter's brush determine the shading of their subject, so does a writer's stroke of a pen determine its depth. A painter paints of inspiration, a writer writes for the same reason; one paints a story with beautiful colors, the other one writes one with colorful words; both start with a blank canvas.
Why writer's write, is a rhetorical question because literally; they can. Anyone taught the skill has the ability and can implement their knowledge onto paper but only a few will master their talent. Only a few will devote the time it takes to gather thoughts and express them in a manner which is art worthy. A devout writer writes to achieve this. A writer constructs his/her dance choreography and song composition from thoughts and ideas. Their dance steps, their paragraphs; their high notes, punctuation marks.
In summation, though expressed in different manners, the same passions running through the veins of other artists run through those of a writer. Writing is their passion. It is a form of expression, consumed by the soul; a form of expression, which he/she must put into practice on a constant basis. They write for no other reason than that.