I think it's telling that fanfiction sees the most pushback from novelists, as opposed to, say, TV creators/writers, comic authors, etc. I'm assuming it's something to do with a) TV/movies/comics/games are more collaborative by their nature and b) since the medium is the same (text), it is harder to negotiate the difference for the pro-writers.

(And personally, I think some writers are insecure and have a fear of someone 'doing it better' that in part feeds their antipathy of fanfic.)