Whether a writer goes to school for writing or does not go to school for writing, it is my opinion that ultimately a writer is always self-taught.
Sure, a formal education never hurts and it can open lots of doors for a writer that a writer would never have an opportunity to pursue if he or she did not have that college degree.
But in the dead of night, when a writer is writing, it is talent that a writer must depend on. Talent is made of a lot of things. And it is built on how serious a writer is about learning his or her craft.
A writer is ultimately self-taught.