That’s a tough question. Obviously writing can be taught, but “good” writing perhaps cannot. Then again, that also depends on your definition of what is good. For example, in some of F. Scott Fitzgerald’s novels I thought his writing was beautiful and eloquent, and in others I really just lost interest.
I think what makes someone a so-called good writer is how hard they’re willing to work at it and how much passion they put into it. If you really love writing and you aspire to get better each and every day, if you try your hardest, then chances are you’re going to improve and get close to, or at, the level of writing you desire.
But yes, I suppose a writer does have to have a “special something.” And that something can be different for every writer and every reader. If you can connect to that writer’s work and their words burn holes within you, if those words consume you and make you truly think, then you would probably consider them to be a good writer. Good writers have a certain essence that attracts their readers.
But it’s also true that you can start out writing horribly and end up writing quite well. Even some of the best writers were rejected from publication countless times before they finally “got it made.” http://www.writersservices.com/mag/m_rejection.htm
So if you want to be a “good” writer, then keep hope. It can happen. <3