But, we've also spent a lifetime practicing our grammar. We haven't spent it trying to write exceptional works. To overcome this, we need a training program to get our brains in shape.
First, we have to be able to recognize good writing. Then, we must exercise by writing and checking to see if it's any good. The only way to teach your brain about good writing, is to read a slew of good writing. While reading, try to edit their writing (What feels wrong? Can you identify why it feels wrong? Are there better constructions? If not, what makes it good?).
With our editor's eye, we can evaluate our writing. All that's left is to push ourselves to write every day. Some suggest trying a different form of writing every day; I like keeping a daily journal. I believe every day brings something worth writing about, we just have to be smart enough to find it.
While this program can be laid out in two paragraphs, it still involves a mind-bogglingly large amount of work. This is usually what prevents people from being great writers. It's too damn much work.