So, the initial question...
Fanfiction: is It Real Writing?
The answer is "yes". Don't let anyone tell you otherwise. Just look at other forms of media...is a photographer any less an artist, even if the model she is photographing is wearing clothes someone else designed? Is a classical musician--who, after all, is just interpreting Mozart and Bach and all the rest and not actually producing new original works--not a musician? Don't be silly. Thus, fanfiction is "real" writing. In fact, when you get to TV show script writing and comics writing, all you're doing is playing in someone else's worlds anyway. The Avengers and the three Batman films recently were pretty popular as I hear it.
It's just that, in this world with the laws we have surrounding transformative works, it's damn hard to make a living out of fanfic based on novels unless you happen to do fanfic of a work that's out of copyright, like the Wizard of Oz series (which inspired the novel Wicked, which inspired the musical Wicked), or you have the drive to get into a shared world. (Although John Scalzi recently managed it, with
Fuzzy Nation...he wrote the fanfic, then approached the original author's estate and got permission to publish it. Lucky him!) Since it's difficult to sell fanfic, and it's derivative, people like to think it's not real writing. Also, fanfic has a low barrier to entry, money and skill-wise, so it gets a plebeian reputation, because a lot of newbies show just how little they absorbed in their school English classes, and the other half write a lot of porn, which is fun at first, but eventually gets tiring and often squicky. So it gets a bad rep.
I write both original fiction and fanfic. I started writing original fic when I was 10 or so, and continued that until my mid-twenties. I did do fanfic in my head at that time, but generally didn't write it down. Then in my mid twenties, I began doing a lot of Dragonriders of Pern fanfic (see D. M. Domini on AO3 and fanfiction.net).
Writing original fiction taught me a lot about worldbuilding from "scratch", and character building from scratch. When I began writing fanfic too, I was able to bring those qualities into fanfiction from the start. However, one thing I was struggling with in original fiction is planning and long-term execution--the world and character building take up SO much brain time it's unbelievable, and it's very easy to get stuck on that. With fanfic, you DON'T have to spend all that time world building. You don't even have to describe the characters much--you rely on the reader having read the original series. And this, for me, makes writing fanfic incredibly easier--AND also allowed me to, for once, focus my efforts on plot, and setting up scenarios. I can't tell you how much this has helped me hone my skills in this area, and how much it's helped my original fiction...once I became less scared of outlining in my fanfic because I had brain cycles left to spare for it (I really, REALLY didn't want to box myself in, in my original fic!) it's let me progress on the original fiction. So doing both has been win-win for me. Also, with the fanfic, I've started to learn to deal with criticism, and how to measure the worth of a negative comment. Some people are talking out their asses, but others have good points and give good input. It's nice to learn how to deal with both.
There's good fanfic out there, there's bad fanfic out there. I think fanfic is an awesome learning tool. I don't think, if you want to be a writer, you should ONLY focus on fanfic because, again, the setup of fanfic is that you don't HAVE to world build, you don't HAVE to create characters from scratch and those are good skills to have too. But I'd never say a fanfiction writer isn't a real writer, or that it's worthless, or that all fanfiction is drek. It's not. It's not that black and white. It's just, as a reader getting into fanfic, you are exposed to the Slush Pile you generally are insulated against in the pro book world , so it's easy to say it's all crap. I'm sure agents and publishers can tell stories of just how much bad original fiction THEY see and pass on all the time.