The reasons most authors frown on fan fiction are legal. If you do not defend your copyright, legally the case can be made that you have abandoned it, and you lose all ability to protect your work.

I also think that doing fan fiction is bad training for any aspiring writer. With the world and the background all provided, the writer does not learn to create these things for himself. Fan fiction is to fiction as paint-by-numbers kits are to painting.

Of course, it is very flattering when someone likes your world so much that they want to write stories in it, and you hate to douse any fan's enthusiasm... but ultimately it's a bad idea, for both fan =and= pro.